cond-mat.stat-mech

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cond-mat.stat-mech 2026-05-13 Recognition

Analytic formulas quantify link fluctuations in extensible chains

Link length and energy fluctuations in extensible freely jointed chains

Asymptotically exact expressions give means, spreads, and distributions of lengths and energies under force.

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The freely jointed chain is often applied to model the thermodynamics of single polymer chains, but the traditional formulation of the model lacks internal energy changes due to bond stretching. For this reason, the extensible freely jointed chain model includes a potential energy function, typically harmonic, that governs the length of each link in the chain. Among the other quantities of interest that are subject to thermal fluctuations, these link lengths and energies too fluctuate about their ensemble average values. Since a plethora of models for polymer chains and networks incorporate chain dissociation as a function of either link length or energy, these fluctuations are crucial to understand and quantify. Motivated by this fact, fluctuations in link length and energy are analyzed within a freely jointed chain under an applied force. These fluctuations are quantified through their average values, standard deviations, and probability distributions. Across all values, asymptotically correct analytic relations and their less ergonomic exact counterparts are introduced. The asymptotic relations are verified to be accurate through direct comparison and to be correct within transcendentally small terms through error analysis. In certain cases, the fluctuations are shown to be approximately normally distributed. Hereafter, model components predicated on link length or energy ought to account for these fluctuations.

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cond-mat.stat-mech 2026-05-13 2 theorems

Diameter dynamics create ultrastable glasses

Identifying the relevant parameters in design strategies for stable glasses

New methods that reach extreme hyperuniformity and local order without size changes produce no stability gain, implicating preparation time-

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A glass is conventionally obtained by cooling a bulk supercooled liquid through its glass transition temperature. The discovery of ultrastable glasses prepared using physical vapor deposition, together with the recent multiplication of numerical algorithms created to increase the stability of glasses, demonstrates the existence of a variety of strategies for designing glasses with different physical properties. This raises a broader question: which parameters most strongly govern the enhancement of glass stability? Existing computational strategies often produce highly stable glasses by optimizing certain physical properties through dynamical changes in particle diameters. We challenge the idea that these physical quantities are causally responsible for glass stability and suggest instead that diameter dynamics is the principal source of enhanced stability. To support our view, we introduce computational methods to optimize physical quantities without changing the particle diameters. Using the examples of enhanced hyperuniformity at large scale and local ordering at small scale, we design glass configurations with highly optimized values compared to bulk equilibrium states. However, these glasses do not show enhanced stability. The proposed physical quantities are correlated with glass stability, but are not causally responsible for ultrastability. These findings indicate that design rules for stable glasses should be reinterpreted in terms of the dynamical processes that generate stability, rather than the optimized physical quantities they target.

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cond-mat.stat-mech 2026-05-13 2 theorems

Fermion thermodynamics reduces to classical particles with built-in attractions

Statistical Potential for Identical Fermions: Emergent Attraction and Pauli Crystal Formation

A collective statistical potential turns attractive for N greater than two and places its minima exactly at Pauli-crystal sites.

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We show that the thermodynamics of $N$ identical fermions maps onto that of distinguishable particles governed by a collective statistical potential -- the microscopic origin of degeneracy pressure. Known to be purely repulsive for ${N=2}$, this potential develops attractive contributions for ${N\geq 3}$. Its minima coincide with Pauli crystal configurations, providing the energetic origin of these structures. For large $N$, the dominant force is attractive on inner shells and repulsive on outer ones -- not of two-body origin. The global minimum undergoes discrete melting transitions at specific temperatures.

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cond-mat.stat-mech 2026-05-13 2 theorems

Non-reciprocity fades at criticality for n>=4 conserved systems

Critical Dynamics of Non-Reciprocally Coupled Conserved Systems

One-loop RG identifies a fixed point where large-scale dynamics obey detailed balance despite microscopic non-reciprocal couplings.

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Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation from equilibrium dynamics. Though common implementations of non-reciprocity lead to such phenomenology, these spatio-temporal patterns are absent in other models. In the same vein, the ensuing scaling behaviour also depends on the precise way non-reciprocity is implemented. To better understand the effects of different non-reciprocal interactions, we study the critical conserved dynamics of non-reciprocally coupled spin systems. Specifically, we consider the dynamics of two $n$-component order parameter fields $\boldsymbol{\phi}_i$ with $i \in\{1,2\}$. Unlike the common implementations of non-reciprocal interactions, we introduce the non-reciprocity solely through the non-linear interaction between the distinct species. Using the field-theoretic renormalisation group (RG) procedure, we perform a one-loop analysis and show that at one-loop level, the critical behaviour depends on the microscopic value of certain quantities. Using the flow functions, we elucidate the behaviour of the fixed points for different bare microscopic values. We also show that for $n \geq 4$, there is a fixed point where the ensuing critical dynamics asymptotically obey detailed-balance, implying the emergent dynamics are agnostic to the microscopic non-reciprocity on large scales. Finally, we show that the conserved dynamics reduces the number of independent scaling exponents, mimicking the effect of a standard fluctuation-dissipation relation.

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cond-mat.stat-mech 2026-05-12 2 theorems

Percolation threshold drops faster near 3D in fractional lattices

Random-h Fractional-Dimensional Lattices Reveal Endpoint-Compressed Percolation Activation between Two and Three Dimensions

High-resolution scans show activation compresses at the three-dimensional endpoint while mass and coordination evolve independently.

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Non-integer dimensionality is central to fractal and complex systems, yet it is rarely represented as an explicit lattice on which classical statistical-mechanical models can be directly simulated. Here we introduce random-h fractional dimension (RhFD), a constructive lattice framework in which fractional-dimensional environments are generated by stochastic activation of local connectivity, h. In the 2D-to-3D interval, RhFD lattices are formed by recursively growing out-of-plane sites from a square base with probability \r{ho}h. Using quenched site-percolation simulations, we show that the construction recovers the integer-dimensional endpoints and yields a robust crossover in which the percolation threshold decreases from the 2D regime toward the 3D regime. The crossover is not a uniform interpolation: high-resolution scans reveal endpoint-compressed activation, with -dpc/d\r{ho}h increasing toward \r{ho}h = 1. Mass dimension increases with \r{ho}h, whereas the coordination descriptor first decreases as sparse protrusions form and then rises sharply when a dense 3D backbone emerges. RhFD provides an explicit lattice substrate for fractional-dimensional statistical mechanics and shows that geometric mass, local coordination, and critical connectivity can decouple during dimensional crossover.

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cond-mat.stat-mech 2026-05-12 2 theorems

FRG treats noise-to-signal ratio as temperature for anomaly detection

Field Theory of Data: Anomaly Detection via the Functional Renormalization Group. The 2D Ising Model as a Benchmark

In the 2D Ising benchmark the method locates critical thresholds with under 4% error by mapping detection to RG flows near the Marchenko-Pa

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We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which we identify with the universal Marchenko-Pastur distribution. Applying the Functional Renormalization Group to the two-dimensional Model A, we demonstrate that the noise-to-signal ratio acts as a physical temperature, where the signal emerges as ordered domains within a thermalized background of fluctuations. Using the exact Onsager solution as a benchmark, we show that this approach identifies critical thresholds with an error below 4%, significantly outperforming standard information-theoretic metrics such as the Kullback-Leibler divergence. Our results provide a universal strategy for resolving structures in complex datasets near criticality, bridging the gap between statistical mechanics and statistical inference.

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cond-mat.stat-mech 2026-05-12 2 theorems

Mitigation inverts epidemic trend on scale-free networks

Susceptible-Infected-Susceptible Model with Mitigation on Scale-Free Networks

At high rates, less heterogeneous networks show higher prevalence than in the standard model.

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We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated through a power-law distribution, while a mitigation factor accounts for behavioral responses and external effects that effectively reduce transmission from infected individuals. This mechanism, inspired by Malthus-Verhulst-type constraints, introduces a nonlinear saturation effect that encodes self-limiting dynamics in a tractable way. Analytical results are supported by stochastic simulations. We find that the mitigation factor induces a nontrivial behavior in the probability that a link points to an infected node, which develops a maximum at finite infection rates. In contrast, the overall prevalence remains a monotonically increasing function of the transmission rate. Additionally, the mitigation mechanism leads to an inversion in the dependence of epidemic observables on the degree exponent at sufficiently high transmission rates. While in the standard model smaller exponents yield higher endemic prevalence, in the modified model this trend reverses, with larger exponents producing higher prevalence and increased infection probability along network links.

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cond-mat.stat-mech 2026-05-12 Recognition

Exact non-Markovian diffusion equation for Gaussian velocities

The diffusion equation for non-Markovian Gaussian stochastic processes

It generalizes the Fokker-Planck equation to arbitrary memory and non-stationary driving while showing position Gaussianity holds only at an

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We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the characteristic function of the density of the position, we construct a systematic hierarchy of equations based on Wick's theorem, in which the dynamics is governed by sums of geometrically connected Wick contractions. This approach yields a closed non-Markovian diffusion equation that generalizes the Fokker-Planck description and preserves Gaussianity only in the infinite-order limit.

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cond-mat.stat-mech 2026-05-12 2 theorems

Bias outweighs neighbor coupling in LLM agent groups

Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics

Statistical-physics analysis of lattice models shows intrinsic bias produces crossovers, not phase transitions, and supplies model-specific

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We investigate the emergent collective dynamics of LLM-based multi-agent systems on a 2D square lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-agent systems. In our framework, each node of an $L\!\times\!L$ lattice hosts an identical LLM agent holding a binary state ($+1$/$-1$, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature $T$ serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe $\mathbb{Z}_2$ symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-$L$ lattices yields effective exponents $\gamma/\nu$ whose values are model-dependent, close to but incompatible with the 2D Ising universality class ($\gamma/\nu=7/4$). Our method enables the extraction of effective $\beta$-weighted couplings $\tilde{J}(T)$ and fields $\tilde{h}(T)$, which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective alignment is dominated by an intrinsic bias ($\tilde{h}\gg\tilde{J}$) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM agents and a quantitative diagnostic for the reliability of multi-agent consensus and collective alignment.

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cond-mat.stat-mech 2026-05-12 2 theorems

Real-time RG reveals chaotic flows in nonunitary quantum dynamics

Renormalization of Quantum Operations: Parity-Time Transition and Chaotic Flows

The measurement-induced parity-time transition is placed in the Yang-Lee edge singularity class, offering a route to simulate imaginary spin

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The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement backaction, in which the notion of conserved energy is absent. Here, we extend the RG to cover nonunitary quantum dynamics governed by quantum operations. By performing coarse-graining in real time, we find that the competition between decoherence and coherent dynamics plays a decisive role in the behavior of the RG flow. In particular, we find that chaotic behavior without fixed points emerges in the RG flow when coherent dynamics is dominant, with the parity-time transition serving as a prototypical example. The measurement-induced parity-time transition belongs to the universality class of the one-dimensional Yang-Lee edge singularity, which serves as a guide for experimentally realizing imaginary fields in lattice spin systems with a quantum system.

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cond-mat.stat-mech 2026-05-12 2 theorems

Monte Carlo data yields N-queens constant γ to high precision

Statistical mechanics of the N-queens problem

Thermodynamic integration of a lattice gas model matches the combinatorial value 1.94400(1) within 0.1 percent at N=1024.

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We investigate the $N$-queens problem as a lattice gas -- a model in which $N$ queens are placed on an $N \times N$ chessboard with pairwise repulsive interactions along shared rows, columns, and diagonals -- from the perspective of statistical mechanics. The ground states are exactly the $Q(N)$ solutions of the classical $N$-queens problem, with entropy per queen $s_0 \approx \ln N - \gamma$ ($\gamma \approx 1.944$). This entropy reflects a characteristic constraint hierarchy: each successive geometric constraint -- columns, then diagonals -- reduces the entropy from the free-placement value $\ln N$ by a definite constant. We derive the exact high-temperature energy $E/N \to 5/3$ as $N \to \infty$. Extensive Monte Carlo simulations with $10^8$ sweeps per temperature point for $N = 8$--$1024$ reveal that the specific heat per queen $C_v/N$ converges to a universal function of $T$ as $N \to \infty$. The converged curve features a non-divergent peak $C_v^{\max}/N \approx 1.63$ at $T^* \approx 0.235\,J$, establishing the absence of a thermodynamic phase transition. Combined with the trivially exact high-temperature entropy $S(\infty)/N = (1/N) \ln \binom{N^2}{N}$, the convergence of $C_v/N$ enables a thermodynamic integration of $C_v/T$ from $T = \infty$ to $T = 0$ that recovers the ground-state entropy -- and hence the Simkin constant $\gamma$ -- purely from Monte Carlo data. This provides an independent thermodynamic route to a fundamental combinatorial constant. Thermodynamic integration yields $\gamma_{\rm MC} = 1.946 \pm 0.003$ at $N = 1024$, within $0.1\%$ of the precise combinatorial value $\gamma = 1.94400(1)$. We further present a transfer-matrix-based tensor network formulation that encodes the non-attacking constraints into a rank-9 site tensor with 17 nonzero elements, providing a complementary exact-enumeration route.

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cond-mat.stat-mech 2026-05-12 Recognition

Monte Carlo data yields Simkin constant γ for N-queens

Statistical mechanics of the N-queens problem

Converging specific heat allows thermodynamic integration to recover ground-state entropy from simulations

abstract click to expand

We investigate the $N$-queens problem as a lattice gas -- a model in which $N$ queens are placed on an $N \times N$ chessboard with pairwise repulsive interactions along shared rows, columns, and diagonals -- from the perspective of statistical mechanics. The ground states are exactly the $Q(N)$ solutions of the classical $N$-queens problem, with entropy per queen $s_0 \approx \ln N - \gamma$ ($\gamma \approx 1.944$). This entropy reflects a characteristic constraint hierarchy: each successive geometric constraint -- columns, then diagonals -- reduces the entropy from the free-placement value $\ln N$ by a definite constant. We derive the exact high-temperature energy $E/N \to 5/3$ as $N \to \infty$. Extensive Monte Carlo simulations with $10^8$ sweeps per temperature point for $N = 8$--$1024$ reveal that the specific heat per queen $C_v/N$ converges to a universal function of $T$ as $N \to \infty$. The converged curve features a non-divergent peak $C_v^{\max}/N \approx 1.63$ at $T^* \approx 0.235\,J$, establishing the absence of a thermodynamic phase transition. Combined with the trivially exact high-temperature entropy $S(\infty)/N = (1/N) \ln \binom{N^2}{N}$, the convergence of $C_v/N$ enables a thermodynamic integration of $C_v/T$ from $T = \infty$ to $T = 0$ that recovers the ground-state entropy -- and hence the Simkin constant $\gamma$ -- purely from Monte Carlo data. This provides an independent thermodynamic route to a fundamental combinatorial constant. Thermodynamic integration yields $\gamma_{\rm MC} = 1.946 \pm 0.003$ at $N = 1024$, within $0.1\%$ of the precise combinatorial value $\gamma = 1.94400(1)$. We further present a transfer-matrix-based tensor network formulation that encodes the non-attacking constraints into a rank-9 site tensor with 17 nonzero elements, providing a complementary exact-enumeration route.

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cond-mat.stat-mech 2026-05-12 2 theorems

Julia package reaches larger many-body eigenpairs with polynomial filtering

Computing eigenpairs of quantum many-body systems with Polfed.jl

Polfed.jl evaluates a spectral transformation on the fly inside Lanczos steps, cutting memory use and enabling bigger system sizes on spin-1

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We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body Hamiltonians. Access to such eigenpairs is essential for studying non-equilibrium many-body physics, but is hindered by the exponential growth of Hilbert-space dimension. POLFED addresses this challenge through a polynomial spectral transformation evaluated on the fly within a Lanczos iteration, preserving Hamiltonian sparsity and substantially reducing memory costs compared to other diagonalization methods. The package supports flexible energy targeting, automatic optimization of the spectral mapping for structured Hamiltonians, and GPU acceleration, which is particularly effective since the dominant computational cost reduces to repeated sparse matrix-vector multiplications. Benchmarks on disordered spin-chain and fermionic models demonstrate access to larger system sizes than alternative approaches, and CPU--GPU comparisons confirm significant speedups. In particular, we also provide code for constructing the quantum sun model Hamiltonian, a toy model of a many-body ergodicity-breaking transition. While our focus is on many-body Hamiltonians, Polfed$.$jl may be applied to any large sparse matrix.

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cond-mat.stat-mech 2026-05-12 Recognition

Planar lattices achieve arbitrarily high Ising Tc

Families of planar lattices with arbitrarily high T_{rm c} for the ferromagnetic Ising model

Iterative triangulation creates families where Tc grows as (2/ln 2) ln qmax and saturates a conjectured optimum.

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We construct families of periodic tessellations of the plane with arbitrarily high critical temperature, $T_{\rm c}$, for the classical ferromagnetic Ising model. Our approach is motivated by recently found exact bounds, which imply that large values of $T_{\rm c}$ require large values of the maximal coordination number of the lattice, $q_{\rm max}$. We create such lattices through iterative triangulation and derive explicit expressions for their $T_{\rm c}$. Furthermore, we show that $T_{\rm c}$ for these families scales asymptotically as $T_{\rm c}/J\sim A \ln q_{\rm max}$ with a universal prefactor $A=2/\ln 2$. We introduce a function $T_{\rm c}^*(q_{\rm max})$ that we conjecture to be optimal for all periodic tessellations of the plane. We show that the family of so-called Apollonian lattices, which are derived from the Triangular lattice through iterative triangulation, saturates this bound. The lattices discussed in this work are relevant for theoretical questions of optimality in network systems and may be realized experimentally in Coherent Ising Machines or topoelectric circuits in the future.

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cond-mat.stat-mech 2026-05-11 Recognition

Noise, speed, and disorder control jamming and separation in active particles

Equilibrium and non-equilibrium properties of active matter systems

Review shows thermal noise, propulsion velocity, and media disorder produce flocking, motility-induced phases, and kinetic arrest in self-

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Active matter systems encompass both natural and artificially created systems consisting of numerous active particles. These particles actively consume energy to propel themselves or exert mechanical forces, leading to intricate behaviors and a diverse range of collective motions from flocking transition to motility-induced phase separation. The flocking transition refers to the spontaneous alignment and coordination of individuals in a group, resembling the cohesive motion observed in flocks of birds or schools of fish. On the other hand, motility-induced phase separation refers to the segregation of active particles into distinct regions based on their differing motility levels. In this presentation, I will talk about active matter systems, specifically focusing on the collective behavior and dynamics, including the influence of volume exclusion features, the impact of disorder in the media, and the behavior of self-propelled particles in off-lattice domains by introducing spin anisotropy. The objective is to understand how the collective behavior of self-propelled particles is affected by various system parameters, including thermal noise, self-propulsion velocity, external field strength, etc. I will furthermore show the phenomena such as jamming, kinetic arrest, motility-induced phase separation, coexisting phases, microphase separation, and phase transitions within the context of active matter models.

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cond-mat.stat-mech 2026-05-11 2 theorems

RG flow converges to line between tricritical and critical fixed points

Effective sextic field theory for tricritical-critical crossover

Three-loop beta functions in the sextic theory show the crossover by attraction to the fixed-point line and permit recovery of non-universal

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Effective field theories provide a suitable framework for both particle physics and statistical physics. We delve deeper into the study of the effective three-dimensional scalar field theory for its application to statistical physics, especially considering the role of the sextic coupling in the tricritical-to-critical crossover. The three-loop renormalization of the mass and the two coupling constants that we perform allows us to obtain, for the first time, the complete renormalization group flow of the couplings in that order. We analyze what universality means in this problem and how we can recover non-universal terms from the renormalization group beta functions. The crossover is realized by the convergence of the renormalization group flow towards the line connecting the tricritical and critical fixed points.

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cond-mat.stat-mech 2026-05-11 Recognition

Union-Jack lattice splits Ashkin-Teller line into two BKT boundaries

Emergent critical phases of the Ashkin-Teller model on the Union-Jack Lattice

An intermediate critical phase with power-law magnetization decay appears between the two transitions.

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The Ashkin-Teller (AT) model is a classic spin model in statistical mechanics. For traditional homogeneous lattices like triangular and kagome lattices, even when frustration exists, the model only has one ferromagnetic-paramagnetic critical line in the $J>0$ and $K<0$ region. However, in this paper, for the Union Jack lattice, where the lattice coordination numbers are 4, 8, and 8 and which also contains a large number of small triangular units, using Metropolis Monte Carlo method, we find that, the critical line of the AT model splits into two Berezinskii-Kosterlitz-Thouless(BKT) boundaries, and a critical phase emerges in the intermediate region. This phenomenon is the combined result of frustration, lattice inhomogeneity and the two coupled spin degrees of freedom inherent to the AT model. In detail, the novel critical phase characterized by a power-law decay of magnetization with system size, where the correlation length ratio $\xi/L$ remains finite even in the thermodynamic limit. We also introduce the susceptibility $\widetilde{\chi} = \text{d}\langle m \rangle /\text{d}J$ as a key probe, and through this probe, pseudo-critical points $J_c(L)$ are observed to scale proportionally to $(\ln L)^{-2}$, a behavior consistent with BKT criticality. Since superfluids, superconductors, and supersolids all possess quasi-long-range order and fall into the category of critical phases, our results could also inspire the exploration of such quantum phases.

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cond-mat.stat-mech 2026-05-11 Recognition

Active particles add two plateaus and f to the minus four scaling to confined spectra

Power spectral density of trajectories of active Ornstein-Uhlenbeck particles

The spectrum reveals double trapping by thermal and active noise plus transient ballistic motion that passive systems lack.

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The power spectral density (PSD) is a central frequency-domain descriptor of stochastic processes. While PSDs have been studied for Brownian motion and a few anomalous diffusion processes, the spectral densities of active nonequilibrium processes remain almost unexplored. Here, we present an exact theory for the PSDs of active diffusion using the model of active Ornstein-Uhlenbeck particles (AOUPs). We investigate the spectral densities of AOUPs in free space and under harmonic confinement. In free space, active motion does not alter the Brownian $f^{-2}$ spectrum, but only modifies its amplitude and introduces a crossover at the persistence frequency. Under confinement, the spectrum exhibits a rich variety of features depending on the persistence, trap relaxation, and activity strength, including two characteristic signatures that are absent in both thermal systems and free AOUPs. These are a two-plateau structure from a double-trapping mechanism due to two noise sources, and the new $f^{-4}$ spectral scaling associated with transient ballistic motion. We also investigate the finite time effects through the finite-time PSD, and find that the low-frequency plateau and high frequency oscillation exhibit distinct dependences on the observation time $T$ in free and confined systems. Finally, we discuss our results in connection with previously reported experimental studies of active systems. Our results provide an analytically tractable framework for interpreting such systems.

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cond-mat.stat-mech 2026-05-11 Recognition

Markov models enable sensitivity estimates despite rare events

Sensitivity Analysis in the Face of Rare Events

Importance sampling plus timescale separation yields efficient derivatives for optimizing molecular motors and similar systems.

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Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the parameters. When the system's dynamics involves rare events, both the observable and its sensitivity are difficult to estimate from direct simulation. We present a practical computational pipeline that addresses both challenges by combining importance sampling with a Markov state model (MSM). The MSM separately captures the slow, rare-event dynamics and the fast, local dynamics, and the chain rule connects those two pieces to yield an efficient sensitivity estimator. An iterative reweighting procedure based on the RiteWeight algorithm substantially reduces approximation errors from the MSM coarse-graining. We validate the approach on diffusion in the M\"uller-Brown potential, where the sensitivity of a transition rate to landscape parameters can be computed exactly. We then use sensitivies to optimize the directional bias of a particle-based model of a catalysis-driven molecular motor.

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cond-mat.stat-mech 2026-05-11 Recognition

Theory optimizes molecular machine designs via flow networks

Nonequilibrium Theory for Molecular Machine Design

CFT Design balances speed, energy, and accuracy by treating cost-benefit tradeoffs and misflows in biomolecular systems.

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Modeling the dynamical flows on networks of biomolecular machines often entails computing node populations and edge fluxes with Master Equations and correlating machine performance with entropy production. But this alone is not sufficient for design, optimization and evolution because it doesn't treat cost-benefit tradeoffs, or small-system misflows (backsteps, futile cycles, ineffective actions), or differential properties for flow design. Here we develop CFT Design, based on the recently developed Caliber Force Theory (CFT). We apply it to: designing faster molecular motors through ``traffic control''; optimizing speed, energy, and accuracy in kinetic proofreaders; and designing better enzyme inhibitors. CFT Design provides a general framework for optimizing nonequilibrium flow networks.

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cond-mat.stat-mech 2026-05-11 2 theorems

Condensation transition emerges below critical entropy in probability simplex

Condensation Transition in Entropy-Constrained Probability Spaces

Most distributions condense with one dominant component when entropy drops below log K minus one plus gamma, offering a route to natural 70

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The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex $\Delta_{K-1}$ defined by a fixed Shannon entropy. We introduce a discretization strategy that assigns equal statistical weight to distinct microstate distributions and enables a combinatorial analysis of the simplex. A condensation phase transition is shown to take place below a critical entropy that scales as $H_c \simeq \log K - 1 + \gamma$ in the thermodynamic limit. For entropy values $H_0 < H_c$, the overwhelming majority of distributions are found in a condensed state, in which a single component captures a macroscopic fraction of the total probability mass while the remaining components form a homogeneous fluid background. These results provide a framework for understanding phenomena such as overconfident predictions in machine learning and the emergence of dominant species in ecology, and suggest that sparsity can arise naturally from entropic constraints in high-dimensional manifolds.

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cond-mat.stat-mech 2026-05-11 2 theorems

Only three constraints produce q-exponential distributions

A Closer Look on the Influence of Constraints Upon the Optimization of the Nonadditive Entropic Functional S_{q}

Maximizing nonadditive entropy S_q yields q-exponentials solely for q' equals 1, q and 2-q, while defining consistent effective temperature.

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The thermal-equilibrium canonical distribution is currently obtained by maximizing the Boltzmann-Gibbs-von Neumann-Shannon entropy $S_{BG}(p)=k\sum^{W}_{i=1}p_{i}\ln 1/p_{i}$ constrained to $\sum^{W}_{i=1}p_{i}=1$ and $\sum^{W}_{i=1}p_{i}\,e_{i}=U$, $e_{1}\leq\ldots\leq e_{W}$ being the energies of the $W$ possible states and $U\in[e_{1},e_{W}]$ their mean value. We revisit a generalized version of this optimization problem grounded in the nonadditive entropy $S_{q}(p)=k\,(\sum^{W}_{i=1}p_{i}^{q}-1)/(1-q)$ (frequently, though not necessarily, $q\in(0,1)$; $S_1=S_{BG}$), and the constraint $\sum^{W}_{i=1} p_{i}^{q^{\prime}}e_{i} / \sum^{W}_{i=1}p_{i}^{q^{\prime}}=U$, $q^{\prime}>0$. Sufficient conditions for existence, strict positivity, and uniqueness of solutions are derived, along with a theorem that enables their closed-form calculation. We apply these results to deepen the understanding of the two standard cases in the literature ($q^{\prime}=1$ and $q^{\prime}=q$), as well as of a new one ($q^{\prime}=2-q$). We prove that these standard cases are the only ones yielding optimizing probability distributions of $q$-exponential form. Furthermore, we define an effective temperature $T_{q,q^{\prime}}$ through a Clausius-like relation $1/T_{q,q^{\prime}}=\partial S_{q} / \partial U$ and derive a Helmholtz-like energy $F_{q,q^{\prime}}=U-T_{q,q^{\prime}}S_{q}$, with the former grounding the validity of the $0^{th}$ Principle of Thermodynamics within this generalized statistical mechanics. Finally, we show that the case with a linear constraint (i.e., $q^{\prime}=1$) with $q\in(0,1)$ (i) preserves the Third Law of Thermodynamics; (ii) can be used to model classical many-body Hamiltonian systems with arbitrarily-ranged interactions; and (iii) resembles features of low-dimensional nonlinear dynamical systems at the edge of chaos.

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cond-mat.stat-mech 2026-05-11 2 theorems

Optimal resetting rate jumps or varies smoothly on a ring

Mirror transitions in diffusion with stochastic resetting confined on a ring

Arc length to target and weight of second resetting site control whether the fastest strategy changes abruptly or continuously, with mirror

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Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the mean first-passage time. While substantial work has focused on the study of the optimal resetting rate in unbounded one dimensional domains, little is still known about the optimization of the mean first-passage time in bounded systems, in particular when multiple resetting sites are available. In this work, we consider a particle diffusing along a circular circumference and under resetting, with an absorbing target site at a fixed location. Using the appropriate free propagator for this system, we compute the Laplace transform of the survival probability when resetting occurs to multiple sites drawn from an arbitrary probability density function. We also calculate the mean first-passage time at the target site, and study the dependence of the optimal resetting rate in terms of the relevant parameters of the system in a two-resetting site configuration. Depending on the arc length between one of the resetting sites and the absorbing target site, and the weight of the remaining resetting site, the optimal resetting rate can exhibit abrupt ("first order'') and continuous ("second order'') transitions. Moreover, the behavior of the mean first-passage time is rich enough to allow both critical and tri-critical points to exist in the parameter space. All the transitions have "mirror symmetry'' around the selected target site and its corresponding diametrically opposite site.

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cond-mat.stat-mech 2026-05-11 2 theorems

Eigenstate matrix elements depend on charge fluctuation scales

Multiscale Structure of Eigenstate Thermalization

Algebraic decay exponents in integrable systems vary non-analytically with ensemble fluctuation magnitude beyond macrostate densities.

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The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate that distributions of matrix elements in macroscopic systems may depend not only on the macrostate parameters, such as the densities of local conserved charges, but generally also on the properties of ensembles used in sampling eigenstates. To this end, we depart from the conventional analysis of microcanonical windows and consider statistical ensembles with an adjustable scale parameter prescribing the magnitude of charge fluctuations. We specifically consider an integrable field theory that permits efficient numerical sampling of matrix elements and reliable extrapolation to the thermodynamic limit. Moreover, in this system, we identify a class of states that enables explicit closed-form computation of the suppression rate of matrix elements. Our findings reveal an underlying multiscale structure of matrix elements captured by a non-analytic fluctuation-scale dependence of algebraic exponents governing their statistical properties.

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cond-mat.stat-mech 2026-05-11 Recognition

Local perturbation creates linear density links across positions

Mutual Linearity in Nonequilibrium Langevin Dynamics

In nonequilibrium Langevin systems a change at one spot produces proportional stationary densities everywhere, plus related linearity for 1D

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Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling and designing nonequilibrium responses in continuous systems. When a dynamical parameter is locally perturbed at a single position, the stationary densities at any two positions are linearly related. It further leads to mutual linearity among different stationary state-current observables. We also extend the mutual linearity to non-stationary relaxation processes in the Laplace domain. Our theory reveals that mutual linearity in both discrete and continuous systems originates from the same one-dimensional response structure. We further show that mutual linearity is robust under finite-width perturbations. As an application, we demonstrate the mutual linearity and its finite-width robustness in the F$_1$-ATPase rotary motor model.

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cond-mat.stat-mech 2026-05-11 2 theorems

Cluster dynamics stay fast until tricriticality

Cluster Dynamics Stay Fast-Until Tricriticality

Hybrid updates keep near-optimal efficiency along the critical line of the Blume-Capel model but revert to local scaling exactly at the tric

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Cluster Monte Carlo algorithms are widely regarded as the most effective route to overcoming critical slowing down in lattice spin systems. Whether this acceleration persists in the presence of vacancies and multicritical fluctuations, however, remains unresolved. We address this question through a systematic dynamic-scaling study of hybrid cluster-local update schemes in the two-dimensional Blume-Capel model, which exhibits a line of continuous Ising-like transitions terminating at a tricritical point. Along the entire critical line, hybrid dynamics retain the near-optimal efficiency of pure cluster updates despite the presence of annealed vacancies. Strikingly, this acceleration collapses precisely at tricriticality, where the dynamic critical exponent reverts to the local-update value. We trace this breakdown to the correlated percolation of vacancies, whose emergent system-spanning geometry obstructs nonlocal relaxation in the spin sector. Our results identify a fundamental geometric limitation of cluster acceleration at tricriticality and establish vacancy percolation as the mechanism controlling dynamic universality in hybrid Monte Carlo dynamics.

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cond-mat.stat-mech 2026-05-11 2 theorems

Branching from negative potentials tames Feynman-Kac kernels

Tamed Feynman-Kac diffusion processes: Killing-branching intertwine

Computer path simulations in 1D double-well models show how sign changes in the potential enable relaxation by compensating killing with new

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Relaxation to equilibrium of a drifted Brownian motion is quantified by a probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kernel of the Schr\"{o}dinger semigroup operator. Although seemingly devoid of a natural probabilistic significance (except for its explicit path integral definition), the pertinent kernel relaxes to equilibrium as well. The implicit Feynman-Kac potential ${\cal{V}}(x)$, continuous, confining and bounded from below, may take negative values. If positive, ${\cal{V}}(x)$ can be interpreted as the killing rate of the decaying diffusion process. In case of relaxing F-K kernels the killing effects are tamed (often overcompensated). The taming inavoidably appears in conjunction with the existence of the negativity subdomains of ${\cal{V}}(x)$ in $R$. If locally ${\cal{V}}(x) < 0$, its sign inversion $- {\cal{V}}(x)$ can be interpreted as the branching (cloning, alternatively bifurcation) rate in the course of the other wise free random motion. The arising killed diffusion processes with branching, we interpret as the possible path-wise background of tamed (relaxing) Feynman-Kac diffusions. We present acomputer-assisted path-wise arguments, towards a consistency of the killing/branching taming scenario, for a number of nonlinear model systems in one space dimension. Special attention is paid to Feynman-Kac potential shapes, presumed to be in the double well form, where an analytic access to eigenvalues and eigenfunctions is scarce beyond the semiclassical regime.

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cond-mat.stat-mech 2026-05-11 2 theorems

n-species exclusion process yields 2n+1 boundary phases

Hydrodynamics and boundary-induced phase transitions in the n-species particle-exchange process

Riemann invariants of the hydrodynamic equations map microscopic boundary rates to explicit stationary phases for any number of species.

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The $n$-species particle-exchange process (PEP($n$)) is an exclusion process in which particles of $n$ different species exchange positions on neighbouring sites with rates chosen such that the invariant measure on the discrete torus is a product measure. We address the large-scale hydrodynamic behaviour of this process which yields a system of $n$ coupled inviscid Burgers equations. This system of conservation laws is shown to admit Riemann invariants for arbitrary $n$ from which explicit solutions of the Riemann problem in terms of shock waves and rarefaction fans are obtained. We also introduce the open PEP($n$), in which particles are exchanged with boundary reservoirs. For a distinguished manifold of boundary rates, we prove that the invariant measure is the same product measure as in the periodic system. The hydrodynamic description in terms of Riemann invariants is used to derive the stationary phase diagram explicitly in terms of microscopic boundary rates. In the generic case, the steady state exhibits $2n+1$ phases, with boundary-induced phase transitions analogous to those of the single-species asymmetric simple exclusion process.

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cond-mat.stat-mech 2026-05-11 Recognition

Spatially modulated asymmetry creates travelling waves

Nonreciprocal McKean-Vlasov Equations: From Stationary Instabilities to Travelling Waves

Two-species McKean-Vlasov models show that weak nonreciprocity varying in space suffices to drive self-organized motion from uniform states.

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Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species nonreciprocal McKean-Vlasov equation derived from an underlying system of interacting stochastic particles. Combining linear stability analysis, weakly nonlinear arguments, pseudo-spectral simulations, and Langevin particle dynamics, we show that the structure of nonreciprocity controls the onset and nature of collective order. For spatially uniform weak nonreciprocity, asymmetry shifts the critical diffusion threshold but produces only stationary instabilities, indicating that uniform imbalance alone is insufficient to generate sustained time-dependent motion. In contrast, spatially modulated nonreciprocity fundamentally enriches the dynamics: depending on its symmetry and coupling to the interaction potential, the homogeneous state can lose stability through Hopf bifurcations, giving rise to standing and travelling wave states. We identify both subcritical and supercritical Hopf transitions, relate the selected patterns to Landau saturation coefficients, and show that travelling waves can emerge even in the weak-nonreciprocity regime without explicit microscopic run-and-chase rules. Direct Langevin simulations confirm that these oscillatory and travelling states persist at the particle level and are not artefacts of the continuum mean-field description. Our results establish nonreciprocal McKean-Vlasov equations as a minimal framework for understanding how spatially structured asymmetric interactions generate self-organized motion, dynamical phase transitions, and nonequilibrium collective order.

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cond-mat.stat-mech 2026-05-08 2 theorems

Tuned rates give exact Bernoulli measure for multi-lane exclusion process

Multilane Asymmetric Exclusion Process with stationary Bernoulli measure

This choice lets currents be written directly in terms of average densities on each lane.

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We consider an Asymmetric Exclusion Process evolving on parallel mutually interacting lanes with neighbouring nearest hoppings of hardcore particles. Number of particles on each lane is conserved. We find a choice of the hopping rates, for which the process has Bernouilli stationary product measure, and calculate the stationary particle currents as a function of average particle densities.

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cond-mat.stat-mech 2026-05-08 2 theorems

Semidefinite programs bound energies of infinite frustrated magnets

Bootstrapping ground state properties of classical frustrated magnets

A hierarchy of convex optimizations brackets ground-state properties from both sides for classical spin lattices.

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We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method, the challenge of non-convex optimization on an infinite lattice is replaced with a hierarchy of finite-size convex optimizations arising from positivity conditions that any probability distribution over spin configurations must satisfy. This adapts the Lasserre hierarchy in the theory of polynomial optimization to the context of frustrated magnetism, and we prove convergence of this hierarchy in the thermodynamic limit. Our method subsumes the Luttinger--Tisza method and further applies to non-quadratic Hamiltonians and non-Bravais lattices, thus addressing limitations of prior analytical methods. We apply the method to various two-dimensional frustrated spin models, where it brackets the energy densities and observables accurately across large parameter ranges with typical run times of seconds per parameter point.

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cond-mat.stat-mech 2026-05-08 2 theorems

Grazing scattering tests conformal invariance directly

Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

A measurable differential constraint on X-ray or neutron cross-sections would verify the symmetry assumed throughout critical phenomena.

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We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification, using e.g. binary alloys, appears well within the existing techniques. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

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cond-mat.stat-mech 2026-05-08

Phase alignment turns chemical drive into sustained rotation

A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling

Rayleigh-like criteria show when entropic and frenetic effects in a coupled probe produce persistent mechanical activity from driven jumps.

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Instabilities in thermodynamic systems are often undesirable, as they can lead to loss of control or even catastrophic behavior. Yet, the same mechanisms can also generate rich nonequilibrium behavior and may play a constructive role in living systems. We introduce a theoretical framework, inspired by Rayleigh's analysis of thermoacoustic instabilities, to study the emergence of mechanical activity. In particular, we derive Rayleigh-like criteria governing the onset of activity and the generation of rotational motion in a slow Newtonian probe coupled to driven chemical processes, described by Markov jump processes. These criteria are expressed in terms of the phase relation between entropic and frenetic contributions, providing a transparent condition for when chemical driving results in sustained rotational or active mechanical motion.

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cond-mat.stat-mech 2026-05-08

Burst timing shapes vesicle signaling activation

Activation in Vesicle-Mediated Signaling Shaped by Batch Arrival Statistics

Different release patterns with identical average rates produce distinct times to reach activation thresholds through fluctuation effects.

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Vesicle-mediated secretion of ions or molecules is a central mechanism of cellular communication, for example in processes such as neurotransmission or hormone release. These events are inherently stochastic: vesicle fusions lead to bursts of variable sizes, releasing discrete packets of transmitters that are subsequently cleared or degraded. The dynamics break time-reversal symmetry due to the interplay of spontaneous bursts and continuous degradation. Using generating functions and a recursion relation, we derive an exact solution for the full time-dependent probability distribution of a general batch arrival-degradation model. This framework also enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation. In particular, different arrival processes with identical mean rates can lead to qualitatively distinct first-passage behavior, reflecting the role of time-asymmetric fluctuations. We also discuss extensions incorporating vesicle depletion. Our results provide a transparent link between stochastic release dynamics and activation timing in vesicle-mediated signaling.

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cond-mat.stat-mech 2026-05-08

Criticality emerges at spinodal points of first-order quantum transitions

Criticality around the Spinodal Point of First-Order Quantum Phase Transitions

Resonant excitations decouple a symmetric subspace, yielding an effective second-order transition with Kibble-Zurek scaling in the tilted Is

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Universality and scaling are hallmarks of second-order phase transitions but are generally unexpected in first-order quantum phase transitions (FOQPTs). We present a microscopic theory showing that quantum criticality can emerge around the quantum spinodal point of FOQPTs where metastability disappears. We demonstrate that, at this instability, resonant local excitations dynamically decouple a Hilbert subspace characterized by an emergent discrete translational symmetry. Projecting the original Hamiltonian onto this subspace yields an effective Hamiltonian that exhibits a genuine second-order quantum phase transition (SOQPT) and the Kibble-Zurek scaling. We validate this framework in the tilted Ising chain which breaks Z_2 symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the FOQPT dynamics is usually governed by an emergent critical point around the quantum spinodal point. Our study establishes a bridge between the dynamics of the FOQPT and SOQPT, and thus sheds new light on the long-standing conundrum of the dynamics of the FOQPT.

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cond-mat.stat-mech 2026-05-08

Ising machines beat Potts machines on Max-3-Cut and Max-4-Cut

Comparative Study of Potts Machine Dynamics and Performance for Max-k-Cut

Tests on large graphs show binary Ising approaches win even where native multi-state Potts encoding should help.

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Combinatorial optimization problems in logistics, finance, energy, and scheduling routinely involve multi-state decision variables. Ising machines (IMs) require binary expansions (e.g., one-hot encoding) to encode such variables, whereas Potts machines (PMs) represent them natively. By doing so, PMs are expected to outperform IMs on multi-state problems. To the best of our knowledge, no systematic study of PM models has yet assessed whether this expectation holds. We therefore benchmark five representative PMs against a reference IM on Max-3-Cut and Max-4-Cut, using 800-vertex GSet graphs and random graphs of up to 50 vertices. Surprisingly, the reference IM still outperforms every PM, and the IM supremacy increases significantly in going from Max-3-Cut to Max-4-Cut. These results provide clear evidence that current PM dynamics underperform relative to binary approaches, even in regimes where they are presumed advantageous. We provide a way forward by quantifying the underperformance of current PMs, as well as by identifying three dynamical properties that correlate strongly with their performance ranking. Our work stresses the need for more systematic assessments of algorithmic performance in order to guide the design of more effective Potts machines.

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cond-mat.stat-mech 2026-05-08 Recognition

Ising machine outperforms every Potts machine on Max-k-Cut

Comparative Study of Potts Machine Dynamics and Performance for Max-k-Cut

The advantage grows larger from k=3 to k=4, showing that native multi-state encoding has not yet produced better dynamics.

abstract click to expand

Combinatorial optimization problems in logistics, finance, energy, and scheduling routinely involve multi-state decision variables. Ising machines (IMs) require binary expansions (e.g., one-hot encoding) to encode such variables, whereas Potts machines (PMs) represent them natively. By doing so, PMs are expected to outperform IMs on multi-state problems. To the best of our knowledge, no systematic study of PM models has yet assessed whether this expectation holds. We therefore benchmark five representative PMs against a reference IM on Max-3-Cut and Max-4-Cut, using 800-vertex GSet graphs and random graphs of up to 50 vertices. Surprisingly, the reference IM still outperforms every PM, and the IM supremacy increases significantly in going from Max-3-Cut to Max-4-Cut. These results provide clear evidence that current PM dynamics underperform relative to binary approaches, even in regimes where they are presumed advantageous. We provide a way forward by quantifying the underperformance of current PMs, as well as by identifying three dynamical properties that correlate strongly with their performance ranking. Our work stresses the need for more systematic assessments of algorithmic performance in order to guide the design of more effective Potts machines.

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cond-mat.stat-mech 2026-05-08

Finite duration optimizes control of noisy Brownian traps

Finite-Time Optimal Control by Noisy Traps

When trap stiffness fluctuates without detailed balance, the shortest-work protocols acquire a nonzero optimal duration that shrinks only at

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The optimal control of passive systems in equilibrium typically favours quasistatic (infinite-time) protocols. We show that a breakdown of quasistatic optimality occurs when the controller itself is dissipative. Concretely, we study a Brownian particle confined by a harmonic trap with stochastically fluctuating stiffness, driven by an external protocol. When these fluctuations violate detailed balance, the probe-controller coupling continuously exchanges work with the system, altering the optimisation landscape. In this regime, optimal protocols are characterised by a finite duration which vanishes above a critical fluctuation strength. This transition can be directly observed in a short-time expansion of the mean work functional. When imposing an endpoint constraint, the transition to zero duration disappears and finite duration protocols remain optimal for all values of the controller fluctuations. These results demonstrate that finite-time optimality can emerge in passive systems under nonequilibrium control.

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cond-mat.stat-mech 2026-05-08

Symmetry blocks restore Gärtner-Ellis for quantum large deviations

Large Deviation Functions for Open Quantum Systems with a Strong Symmetry

Nonanalytic global SCGF is bypassed by minimizing local rate functions obtained inside operator-space blocks, justified by dissipative-freez

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In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the G\"artner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this issue, we propose that the theorem remains valid within blocks of the systems' operator space: we first obtain local rate functions for each block via the theorem and then recover the global one by minimization. This approach is justified by the dissipative freezing phenomenon in such systems. We demonstrate the scheme in an analytical model and a three-spin model with XX interaction. In the latter, we find that the vanishing of a nonanalytic point in the global SCGF under dephasing appears as an avoided ``level'' crossing, and we quantify this behavior using a degenerate perturbation theory.

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cond-mat.stat-mech 2026-05-08

Irreversibility creates emergent conservation laws in reaction networks

Emergent conserved quantities via irreversibility

A derived law connects co-production, broken cycles, and additional conservations, extending the standard index used for model inference.

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Conserved quantities increasingly underpin the inference of physical models. Recently new conserved quantities have been found in this context, that currently lack an interpretation. Here, we show that irreversible reactions in CRNs and Markov Chains lead to emergent conservation laws and broken cycles. Linearly dependent currents - characterized by the "co-production index" - arise due to irreversible reactions. We derive a law relating conserved quantities, broken cycles, and co-production. This resolves a recent conundrum posed by a machine-discovered candidate for a non-integer conservation law. Our findings introduce heretofore overlooked extensions to a widely used index law for CRNs and Markov Chains that undercounts conservation laws. This furnishes new tools and immediate applications for the inference and analysis of models based on conservation laws.

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cond-mat.stat-mech 2026-05-08

Critical energy variance saturates at finite value in disordered Baxter model

Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model

Relative variance grows with size and stays nonzero in the large-system limit for both signs of disorder.

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We investigate the first two moments of the critical internal energy $E$ in a weakly disordered two-dimensional Baxter eight-vertex model as a function of the system size $L$, evaluated at the pseudo-critical point. Disorder is introduced via an equivalent representation of the pure eight-vertex model in terms of two ferromagnetic Ising models coupled by a four-spin interaction of strength $g_0$, where the Ising couplings consist of a uniform ferromagnetic part $J>0$ supplemented by weak Gaussian spatial disorder. In the critical regime, the model is formulated in terms of interacting Grassmann-Majorana spinor fields with quartic interactions and analyzed, for small positive $g_0$, using a combination of replica and renormalization-group methods. We also run extensive numerical simulations measuring the critical internal energy. Our results show that its relative variance increases with $L$ and approaches a finite constant as $L \to \infty$ for both $\pm g_0$. Hence, fluctuations remain relevant independently of the sign of $g_0$ (and thus of the specific-heat exponent), implying a lack of self-averaging of both the critical internal energy and the free energy. Consequently, reliable estimates of these quantities require averaging over many disorder realizations. In addition, we numerically confirm earlier predictions concerning the absence of self-averaging of the critical internal energy in the disordered Ising model.

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cond-mat.stat-mech 2026-05-08

Coupling deforms quantum ring spectrum to trigger thermomechanical effects

Thermodynamics and emergent thermomechanical response of a quantum ring with nonminimal spin--orbit coupling

Spectral deformation imprints on thermodynamic quantities with Fermi statistics generating instabilities and sign changes like mesoscopic

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We investigate the thermodynamic and emergent thermomechanical properties of fermions confined to a one-dimensional quantum ring with effective spin--orbit interactions induced by nonminimal couplings to antisymmetric tensor fields. Using the exact spectrum obtained in the companion work, we develop canonical and grand-canonical descriptions and show that the coupling parameter~$\xi$ deforms the angular-momentum branches, reorganizing the low-energy spectrum and leaving clear signatures in the internal energy, entropy, heat capacity, and spin--orbit response functions. We also formulate an effective thermomechanical description by treating the ring circumference as a quasi-static thermodynamic variable. This leads to a pressure-like quantity and associated response coefficients, directly linked to the microscopic spectrum. In the grand-canonical ensemble, Fermi statistics strongly enhance the response, producing coupling-dependent instabilities and sign changes reminiscent of mesoscopic de~Haas--van Alphen oscillations. Finally, we introduce a phenomenological interacting extension based on an exponential resummation of the free energy, showing that collective effects can sharpen the thermomechanical response and induce anomalous thermal contraction. Our results connect spectral deformation, finite-size thermodynamics, and emergent mechanical behavior in spin--orbit-active quantum rings.

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cond-mat.stat-mech 2026-05-07

Fermi gas hole probability transitions at u=2/π

A transition in the hole probability at finite temperature for free fermions in d dimensions

Exact scaling function Φ_d(u) in any dimension shows order-3/2(d+1) change in fluctuation mechanism due to density gap

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In a free Fermi gas at temperature $T$ much higher than the Fermi temperature one expects that the fluctuations of the number of particles in a given region has Poissonian/classical statistics. On the other hand at low temperature the Pauli exclusion principle leads to non trivial counting statistics. It is of great interest from a theoretical and experimental point of view to characterize the crossover between these two limits. Here we focus on the hole probability $P(R,T)$, i.e. the probability that a region of size $R$ is devoid of particles, in dimension $d$, and on the case of a spherical region of large radius $R$. We show that at low temperature it takes the scaling form $P(R,T)\sim \exp\big[-(k_F R)^{d+1}\Phi_d(u=2R\,T/k_F)\big],$ where $k_F$ is the Fermi momentum. By mapping the problem to an effective Coulomb gas, we compute exactly the scaling function $\Phi_d(u)$ in any dimension. Remarkably, it exhibits a transition of order $\tfrac{3}{2}(d+1)$ at the universal critical value $u_c=2/\pi$, signaling a sharp change in the mechanism of rare fluctuations, associated with the emergence of a macroscopic gap in the optimal density of the associated Coulomb gas. Our analytical predictions are supported by precise numerical evaluations of the corresponding Fredholm determinants.

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cond-mat.stat-mech 2026-05-07

Frustrated particles on spheres reduce to RP2 rotor dynamics

Frustrated Fields: Statistical Field Theory for Frustrated Brownian Particles on 2D Manifolds

Simulations show density rings whose slow orientation follows the one-parameter nonlinear sigma model on the projective plane.

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We develop a statistical field theory that describes the large-N limit of a system of Brownian particles with quenched random pairwise interactions on a compact two-dimensional Riemannian manifold. The resulting Frustrated Fields (F2) model is a non-linear field theory for a smooth self-interacting density field $\rho$ on the manifold, with local and non-local (in space and time) self-interactions characteristic of spin-glass dynamics. Particle simulations show \emph{adiabatic dimension reduction}: on $S^2$, the density concentrates on a slowly precessing great-circle ring whose orientation is a director ($\hat{\mathbf{n}} \sim -\hat{\mathbf{n}}$, even profile). Conditioned on this simulation-supported ring saddle and on a Born-Oppenheimer separation between the slow orientation and the gapped density fluctuations, symmetry fixes the low-energy dynamics to be the nonlinear sigma model (NLSM) on the real projective plane $S^2/\mathbb{Z}_2 = \mathbb{RP}^2$ (the $\mathbb{RP}^2$ NLSM on the projective rotor space) in $(0+1)$ dimensions, governed by a single low-energy constant, the rotational diffusion coefficient $D_{\text{rot}}$. With $D_{\text{rot}}$ and the static ring profile $f_0$ measured from particle simulations, the resulting effective theory reproduces multiple independent orientation- and density-sector diagnostics with no further adjustable parameters.

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cond-mat.stat-mech 2026-05-07

Disorder leaves measurement-induced transitions unchanged in fermions

Measurement-induced phase transitions in disordered fermions

The same nonlinear sigma model applies, with only parameter shifts, so transitions persist in d>1 but not in d=1.

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Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder: in spatial dimensions d>1, a transition occurs between an area x log law phase and an area law phase, whereas in d=1, the system exhibits only an area law phase and no transition. Numerical results further demonstrate that both clean and disordered one-dimensional free fermions exhibit area-law behavior when the system size is large enough.

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cond-mat.stat-mech 2026-05-07

Rapid Rényi-1 saturation forces extensive charge variance

Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking

For continuous symmetries this supplies a static link between nonlinear order and measurable block-charge indefiniteness.

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Strong-to-weak spontaneous symmetry breaking (SWSSB) is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic. We show that, for continuous symmetries, long-range R\'enyi-1 correlator, together with a sufficiently rapid approach to its nonzero asymptotic value, forces subsystem charge indefiniteness: the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature. This gives a precise static fluctuation footprint of charge scrambling. We construct examples to show that the implication is conditional and non-reversible: dephased superfluids retain R\'enyi-1 SWSSB with subextensive charge variance when the R\'enyi-1 tail is too slow, while sparse fixed-charge projectors have extensive charge variance but no local charge-transfer R\'enyi-1 order or long-range conditional mutual information. Finally, we introduce a \emph{twist overlap} correlator, which serves as an analogue of charge variance applicable to both discrete and continuous symmetries. This naturally decomposes local block-charge fluctuations into strong- and weak-symmetry channels. We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner--Yanase skew information. Taken together, these results give a unified understanding for distinguishing nonlinear SWSSB order, local charge indefiniteness, and coherent charge fluctuations.

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cond-mat.stat-mech 2026-05-07

Observables develop kinks at the onset of oscillations

Singular Behavior of Observables at Hopf Bifurcations

Phase averaging over limit cycles creates derivative discontinuities in time averages at supercritical Hopf points

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Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of oscillations. The origin of this behavior is geometric: phase averaging over the emergent periodic attractor eliminates odd powers of the oscillation amplitude, while the squared amplitude varies smoothly with the distance from the bifurcation. Consequently, the excess of any smooth time-averaged observable admits an integer-power expansion; observables remain finite but display discontinuities in finite-order derivatives. This yields an Ehrenfest-like hierarchy of Hopf singularities, in which the first nonanalytic derivative is determined by the lowest-order coupling between the observable and the limit-cycle waveform that survives phase averaging. Generic observables therefore exhibit kink singularities, while symmetry or geometric cancellations can suppress lower-order couplings and shift nonanalyticity to higher derivatives. We demonstrate this mechanism in chemical, electronic, and climate oscillators. Our results identify supercritical Hopf bifurcations as a universal mechanism for nonanalytic observable behavior, where singular features arise without any underlying singular stationary state. They thus provide a generic setting for singular behavior without divergence.

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cond-mat.stat-mech 2026-05-07 Recognition

Time averages develop kinks at Hopf bifurcations

Singular Behavior of Observables at Hopf Bifurcations

Phase averaging over the limit cycle creates derivative discontinuities in observables even though the stationary state stays smooth.

abstract click to expand

Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of oscillations. The origin of this behavior is geometric: phase averaging over the emergent periodic attractor eliminates odd powers of the oscillation amplitude, while the squared amplitude varies smoothly with the distance from the bifurcation. Consequently, the excess of any smooth time-averaged observable admits an integer-power expansion; observables remain finite but display discontinuities in finite-order derivatives. This yields an Ehrenfest-like hierarchy of Hopf singularities, in which the first nonanalytic derivative is determined by the lowest-order coupling between the observable and the limit-cycle waveform that survives phase averaging. Generic observables therefore exhibit kink singularities, while symmetry or geometric cancellations can suppress lower-order couplings and shift nonanalyticity to higher derivatives. We demonstrate this mechanism in chemical, electronic, and climate oscillators. Our results identify supercritical Hopf bifurcations as a universal mechanism for nonanalytic observable behavior, where singular features arise without any underlying singular stationary state. They thus provide a generic setting for singular behavior without divergence.

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cond-mat.stat-mech 2026-05-07

Rigorous asymptotics proven for constrained lattice tadpoles

Lattice Tadpoles

Growth rates of lassos hold when heads are unknotted or tails pierce the spanned surface.

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We prove several rigorous results about the asymptotic behaviour of the numbers of tadpoles (or lassos) embedded in a lattice, including cases where the head is subject to a constraint like being unknotted, or where the tail pierces the surface spanned by the head.

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cond-mat.stat-mech 2026-05-07

Kink correlations depend only on KZ length for superlinear quenches

Kink-kink correlations in nonlinear quenches across a quantum critical point

In the Ising chain algebraic quenches introduce a dephasing scale except when superlinear, yielding compressed-exponential decay that tracks

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When a quantum system exhibiting a second order phase transition is quenched across the critical point in large but finite time, the dynamics are not adiabatic in the critical region and the Kibble-Zurek (KZ) mechanism provides a framework to determine local observables such as the mean defect density. However, to find higher-point functions, one has to go beyond the KZ paradigm asshown in recent works on one-dimensional transverse field Ising model (TFIM) following a linear quench. It has been found that (i) besides the KZ scale, the quench dynamics depend on another length scale that arises due to the finite phase difference between the low energy modes, and (ii) contrary to the expectations based on the KZ mechanism, in general, the correlation functions do not decay exponentially with distance. Motivated by these results for the linear quench, we are interested in understanding if these properties are universal, and consider the 1D TFIM when the transverse field varies algebraically in the vicinity of the critical field. We focus on the equal-time,longitudinal kink-kink correlation function at the end of the quench from the paramagnetic to the ferromagnetic phase, and find that (i) the correlator depends only on the KZ length for superlinear quenches, otherwise an additional dephasing length is required to describe it, and (ii) the dephased correlator decays as a compressed exponential with an exponent that changes continuously with the quench exponent. Our results are obtained using an adiabatic perturbation theory, analytical arguments and exact numerical integration of the relevant equations.

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cond-mat.stat-mech 2026-05-07 2 theorems

Nonlinear operator sets Tsallis q from feedback exponents

Emergence of Tsallis Statistics from a Self-Referential Nonlinear Operator: A Variational Framework

Free-energy minimization with self-consistency entropy recovers the q-exponential whose index equals alpha plus beta without separate postu

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We develop a variational thermodynamic framework for statistical systems governed by a self-referential nonlinear operator Omega characterized by structural exponents alpha > 0, beta >= 0, a symmetric kernel K, and a self-coupling constant kappa >= 0. The central object is the self-consistency entropy S[Psi] = -D_KL(Psi || Omega Psi), which vanishes at the fixed points of Omega and serves as a natural Lyapunov functional. Within the local kernel (mean-field) approximation, minimization of the free energy F = U - T S admits the Tsallis q-exponential distribution as an equilibrium state, with the entropic index q = alpha + beta emerging directly from the fixed-point structure of the operator rather than being postulated. The framework yields a consistent thermodynamic description, including a generalized equation of state PV = (2 - q) T, response functions, and a critical temperature associated with spontaneous symmetry breaking. The relation q = alpha + beta connects independently measurable structural exponents of the feedback mechanism to the observed tail index, providing a parameter-free criterion that distinguishes this approach from superstatistics, constrained entropy maximization, and q-deformed formalisms. This work establishes an operator-theoretic foundation for nonextensive statistical mechanics in which nonlinear self-referential feedback naturally generates Tsallis statistics in the mean-field limit.

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cond-mat.stat-mech 2026-05-07

Power spectrum equals quadratic form of same-frequency responses

Nonequilibrium Fluctuation-Response Theory in the Frequency Domain

Single identity for Langevin and jump processes recovers equilibrium theorems and yields frequency-dependent uncertainty bounds.

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We develop a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The relation expresses the power spectrum of general observables exactly as a quadratic form of local responses measured at the same frequency, thereby extending static nonequilibrium fluctuation-response relations to finite frequencies. The decomposition is spatial for Langevin systems and edge-resolved for Markov jump processes, and applies uniformly to state-dependent observables, current-like observables, and their combinations. As consequences of the same identity, we derive frequency-domain response uncertainty relations, kinetic and thermodynamic uncertainty relations, the equilibrium fluctuation-dissipation theorem, and Harada-Sasa-type relations. Applications to stochastic networks and driven diffusive systems illustrate how the theory resolves fluctuation spectra into edge-wise contributions and reveals frequency-dependent tradeoffs between fluctuations, response, and dissipation.

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cond-mat.stat-mech 2026-05-07

Mass fluctuations drive anomalous diffusion in active particle clusters

Role of mass fluctuations in the diffusion of clusters of Brownian particles with activity

A new term from fluctuating cluster size adds to the usual 1/N scaling and produces D ~ N^{-0.63} matching simulations.

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Motivated by the anomalous diffusion observed in clusters of active Brownian particles (ABPs), where the center-of-mass diffusion coefficient scales as $D\sim N^{-1/2}$ with respect to the number $N$ of particles in the cluster, we derive a minimal theoretical framework starting from the single-particle Langevin equations. The model consists of two coupled stochastic equations: one for the cluster center-of-mass trajectory and one for the mass evolution $N(t)$, explicitly accounting for stochastic displacements induced by particle attachment and detachment. We specialize and validate the framework against ABP simulations of isolated clusters in stationary conditions, where $N(t)$ follows a Gaussian process with mean $N_0$, variance $\propto N_0^\beta$, and persistence time $\propto N_0^\kappa$. Analytical solution of the coupled equations yields the long-time diffusion coefficient as the sum of two contributions: a conventional term $\propto N_0^{-1}$) due to thermal noise plus summation of active forces, and a fluctuation-driven term $\propto N_0^{-\delta}$ with $\delta=2-2/d-\beta+\kappa$, where $d$ is the spatial dimension. We demonstrate that anomalous scaling emerges whenever the second term becomes dominant. The model predicts $D\sim N^{-\alpha}$ with $\alpha=0.63\pm0.06$, in good quantitative agreement with large-scale ABP simulations.

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cond-mat.stat-mech 2026-05-07

Coupled entropy uniquely satisfies uncertainty and extensivity for complex systems

The unique, universal entropy for complex systems

It measures uncertainty where the log-log slope equals -1 and stays extensive across all Hanel-Thurner scaling classes.

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An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution, where the log-log slope equals $-1$. Additionally, entropy must be extensive across the full universality scaling classes defined by Hanel-Thurner. The coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements. The non-additivity of the entropy is equal to the long-range dependence or nonlinear statistical coupling. The entropy-matched extensivity is a function of the coupling, stretching parameter, and dimensions. Evidence is provided that the Tsallis $q$-statistics creates misalignment in the physical modeling of complex systems. Information thermodynamic applications are reviewed, including measuring complexity, a zeroth law of temperature, the thermodynamic consistency of the coupled free energy, and a model of intelligence in non-equilibrium.

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cond-mat.stat-mech 2026-05-07 2 theorems

Coupled entropy uniquely fits all complex-system scaling axioms

The unique, universal entropy for complex systems

It measures uncertainty where the maximizing distribution has log-log slope of -1 and remains extensive across every Hanel-Thurner class.

abstract click to expand

An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution, where the log-log slope equals $-1$. Additionally, entropy must be extensive across the full universality scaling classes defined by Hanel-Thurner. The coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements. The non-additivity of the entropy is equal to the long-range dependence or nonlinear statistical coupling. The entropy-matched extensivity is a function of the coupling, stretching parameter, and dimensions. Evidence is provided that the Tsallis $q$-statistics creates misalignment in the physical modeling of complex systems. Information thermodynamic applications are reviewed, including measuring complexity, a zeroth law of temperature, the thermodynamic consistency of the coupled free energy, and a model of intelligence in non-equilibrium.

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cond-mat.stat-mech 2026-05-07

Random walks spread identically on every finite 2D lattice

Finite-size scaling properties of classical random walk on various two-dimensional lattices

Standard deviation of distance and fractal dimensions remain unchanged across square, honeycomb and other connectivities.

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We consider various two-dimensional lattices such as square, Kagome, Lieb, honeycomb, dice lattices of finite extent, to study the effect of lattice profile in terms of the number of nearest neighbour and connectivity patterns on the classical random walk in the unbiased scenario. We find that the standard deviation of distance travelled by the walker is insensitive to the non-uniformity of the lattice profile leading to diffusive transport even in the finite size lattices. Our study indicates that the mass fractal dimension varies within a window $1.50\pm 0.03$ for all finite-size lattices. A weak ordering within the above window, correlated with the average coordination number, is observed, while Lieb and square lattices yielding the minimum and maximum values, respectively. However, confidence intervals reveal substantial statistical overlap for several lattice pairs even though the lattice profiles vary as far as the average number of connecting bonds and directionality of bonds are concerned. We also study the scaling complexity of the circumference of the closed curve traced by the walker while investigating the hull dimension. We find similar trend for hull fractal dimension as well and that was found to within the window $1.37\pm 0.03$ for finite-size lattices. Within the above window, the ordering remains qualitatively unaltered as compared to mass dimension while the confidence interval rectifies the order quantitatively. The square lattice clearly exhibits the upper bound for hull fractal dimension and the remaining lattices show extensive statistical overlap within the above window. We exhibit a tendency of the mass and hull fractal dimension to reach their thermodynamic values given by Brownian motion when we allow more number of steps within the finite size of the lattice, as confirmed by a data collapse analysis.

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cond-mat.stat-mech 2026-05-07

Monte Carlo sampling estimates theta-graph critical exponents

Random sampling of self-avoiding theta-graphs

Results for arm-length distributions in 2D and 3D lattices support a conjecture for equal-length arms and allow comparison to knot exponents

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Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a combination of the Wang-Landau Monte Carlo method with a variant of the BFACF algorithm which accommodates vertices of degree 3. This allows us to estimate the critical exponents governing the number of theta-graphs and the distributions of the different arm-lengths. For the cubic lattice these values can be compared to the corresponding exponents for prime knots. We also study the number of `monodisperse' theta-graphs where the three arms have the same lengths, and find evidence supporting a conjecture for the critical exponent in two dimensions.

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cond-mat.stat-mech 2026-05-06

Relaxation gap bounds entropy production in driven Markov systems

Information-Geometric Signatures of Nonconservative Driving

The mismatch between KL-divergence acceleration and Fisher information yields a lower bound on steady-state dissipation that is tightest on

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We propose an information-geometric signature of nonconservative driving that detects violations of detailed balance using the Kullback--Leibler divergence and the Fisher information. For Markov jump processes satisfying detailed balance, we show that, near equilibrium, the acceleration of the Kullback--Leibler divergence relative to the equilibrium state is given by twice the Fisher information with respect to time. In contrast, for relaxation toward a nonequilibrium steady state, this relation is generally violated even near the steady state. We refer to the resulting discrepancy as the relaxation gap and derive a lower bound on the steady-state entropy production rate in terms of this gap. We demonstrate that this bound is particularly tight for networks with simple cyclic topologies. Finally, we show that analogous relations and bounds hold for Fokker--Planck dynamics.

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cond-mat.stat-mech 2026-05-06

Disorder shifts optimal grid paths most at low trap densities

Optimal Navigation in Stochastic and Disordered Gridworlds

KL divergence measure of policy change peaks early with trap concentration in weak-bias navigation.

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Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes optimal navigation remain elusive. To address this question, we investigate the navigation of a Brownian particle in a disordered energy landscape, modeled as a lattice with randomly distributed traps. Using dynamic programming, we compute the optimal navigation policies that minimize the mean first-passage time to a target site. To quantify the impact of disorder, we introduce a density of change from a Kullback-Leibler divergence, which captures how the optimal policy is reshaped by either the presence of disorder or the knowledge of its configuration. Our results reveal a non-monotonic dependence of the change of the policy on trap concentration, with a pronounced maximum. In the fluctuation-dominated regime where the navigation bias is weak, we derive an analytical expression for the density of change, and demonstrate that the maximum occurs unexpectedly at low trap concentrations.

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cond-mat.stat-mech 2026-05-06

Enhanced sampling CVs transformed into interpretable protein domain distances

From Enhanced Sampling to Human-Readable Representations of Protein Dynamics

A post-analysis method turns machine-derived collective variables into geometric descriptors that match known states across proteins like KR

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Understanding protein conformational dynamics is essential for elucidating biological function but remains challenging due to the wide range of timescales and the complexity of collective motions. Enhanced sampling methods overcome timescale limitations of conventional molecular dynamics, yet their effectiveness depends on the choice of collective variables (CVs), which are often difficult to define and may lack physical interpretability. In particular, collective variables derived from machine learning or collective vibrational modes can efficiently capture slow dynamics but are not easily mapped onto intuitive structural descriptors. Here, we present a fully automated framework that transforms enhanced sampling trajectories into human-readable representations of protein dynamics. Our approach combines enhanced sampling along CVs derived from frequency-selective anharmonic mode analysis with a post hoc analysis of biased trajectories using weighted dynamic cross-correlation matrices. From these, we identify residue pairs and domains exhibiting correlated and anti-correlated motions, yielding simple domain-domain distances that serve as physically interpretable CVs. We apply this method to five proteins, including KRAS and HIV-1 protease, and show that it consistently identifies biologically relevant domains and motions without prior system-specific knowledge. Projection onto these distances produces free energy surfaces that reproduce known conformational states with low statistical uncertainty while maximizing independent dynamical information. This workflow enables systematic recasting of complex CVs into simple geometric descriptors without loss of essential dynamics. Its generality and automation make it broadly applicable for interpreting enhanced sampling simulations and generating interpretable conformational ensembles for integration with emerging machine learning approaches.

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cond-mat.stat-mech 2026-05-06 1 theorem

Simple domain distances from complex protein simulation variables

From Enhanced Sampling to Human-Readable Representations of Protein Dynamics

Automated post-analysis turns enhanced sampling outputs into interpretable geometric descriptors matching known states.

abstract click to expand

Understanding protein conformational dynamics is essential for elucidating biological function but remains challenging due to the wide range of timescales and the complexity of collective motions. Enhanced sampling methods overcome timescale limitations of conventional molecular dynamics, yet their effectiveness depends on the choice of collective variables (CVs), which are often difficult to define and may lack physical interpretability. In particular, collective variables derived from machine learning or collective vibrational modes can efficiently capture slow dynamics but are not easily mapped onto intuitive structural descriptors. Here, we present a fully automated framework that transforms enhanced sampling trajectories into human-readable representations of protein dynamics. Our approach combines enhanced sampling along CVs derived from frequency-selective anharmonic mode analysis with a post hoc analysis of biased trajectories using weighted dynamic cross-correlation matrices. From these, we identify residue pairs and domains exhibiting correlated and anti-correlated motions, yielding simple domain-domain distances that serve as physically interpretable CVs. We apply this method to five proteins, including KRAS and HIV-1 protease, and show that it consistently identifies biologically relevant domains and motions without prior system-specific knowledge. Projection onto these distances produces free energy surfaces that reproduce known conformational states with low statistical uncertainty while maximizing independent dynamical information. This workflow enables systematic recasting of complex CVs into simple geometric descriptors without loss of essential dynamics. Its generality and automation make it broadly applicable for interpreting enhanced sampling simulations and generating interpretable conformational ensembles for integration with emerging machine learning approaches.

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cond-mat.stat-mech 2026-05-05

Entropy production fluctuations detect criticality more sharply than responses

Universal criticality of entropy production in chemical reaction networks

A bound derived for chemical reaction networks shows that responses can remain finite while fluctuations diverge at bifurcations.

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Stochastic thermodynamics gives universal relations for microscopic entropy production, yet its critical behavior at macroscopic nonequilibrium transitions remains unclassified. We study well-mixed reversible chemical reaction networks in the macroscopic-first limit, where transitions arise as local bifurcations of mass-action dynamics. Using linear-noise formulas, center-manifold normal forms, and Floquet theory, we obtain generic exponents for entropy-production fluctuations and responses at pitchfork, transcritical, saddle-node, and Hopf bifurcations. Beyond this low-order classification, a trajectory-space Cram\'{e}r-Rao type bound yields the universal scaling inequality $\alpha - 2\beta \geq 0$. Hence divergent responses require divergent fluctuations, but not conversely, making entropy-production fluctuations a sharper probe of nonequilibrium criticality.

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cond-mat.stat-mech 2026-05-05

Electric field leaves Kubo fluctuation-dissipation theorem unchanged

Non-Markovian entropy production fluctuation theorem driven by a time-dependent electric field

Induced force on particle and bath preserves the relation, keeping the detailed fluctuation theorem for entropy production valid.

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Fluctuation theorems are key to understanding both fundamental and applied aspects of non-equilibrium thermodynamics of small systems. We study the non-Markovian entropy production fluctuation theorem for the diffusion process of charged particles in a gas inside a harmonic potential and under the action of a time-dependent electric field, using a generalized Langevin equation. By considering the influence of the electric field on both the tagged Brownian particle and the bath particles, an "induced" electric force arises. Despite the additional force, we demonstrate that Kubo's second fluctuation-dissipation theorem (FDT) remains unchanged. The FDT allows us to obtain the Gaussian probability density for the position along a single stochastic trajectory, which is the key to demonstrating the validity of the detailed fluctuation theorem (DFT) for the total entropy production. We study the specific result of an Ornstein-Uhlenbeck-type friction memory kernel and an oscillating electric field, and analyze the average work and entropy production in different parameter regimes.

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cond-mat.stat-mech 2026-05-05 2 theorems

Exact entropy and temperature for any number of equispaced levels

Exact Microcanonical Formulation and Thermodynamics of Equispaced Finite-Level Systems

Saddle-point analysis of the generating-function coefficient yields closed microcanonical expressions that cover arbitrary p and recover all

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We present an exact microcanonical formulation, in the thermodynamic limit, for a system of $N$ noninteracting particles with $p$ equally spaced energy levels $\{0,\epsilon,2\epsilon,\ldots,(p-1)\epsilon\}$. Writing the microcanonical multiplicity $\Omega_p(E,N)$ as the coefficient of a generating function and evaluating the resulting representation by saddle-point analysis, we derive analytical expressions for the entropy per particle $s(u,p)$ and inverse temperature $\beta(u,p)$, with $u=E/(N\epsilon)$ in the interval $[0,p-1]$. The formulation applies to arbitrary $p$ and recovers the known cases $p=2$, $p=3$, and $p\to\infty$. For finite $p$, the bounded spectrum implies an entropy maximum at $u_c=(p-1)/2$, where $\beta$ vanishes and changes sign. In the limit $p\to\infty$, the upper spectral bound is lost, the finite-energy entropy maximum disappears, and no negative-temperature branch remains. To our knowledge, this is the first general thermodynamic-limit microcanonical solution for arbitrary $p$. It therefore provides a unified framework for the thermodynamics of equispaced finite-level systems and their bounded-spectrum crossover with increasing $p$.

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cond-mat.stat-mech 2026-05-05 3 theorems

Power-efficiency frontier of Carnot-like engines found by linear programming

Geometric Formulation of Power-Efficiency Bounds in Carnot-like Engines

Straight-line efficiency contours turn fixed-power maximization into a slope bound that linear programming solves exactly for power-law loss

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We formulate the power-efficiency constraint of Carnot-like heat engines as a geometric optimization problem in the plane of normalized branch dissipations. Efficiency contours are straight lines in this plane, so maximizing efficiency at fixed power reduces to bounding the slope of an admissible line. We apply this framework to branch-resolved power-law dissipation, where the irreversible loss on each isothermal branch decays with the branch duration with a common exponent rather than following the standard inverse-time law. After optimizing over the dissipation-asymmetry parameter, the fixed-power attainable set becomes a two-dimensional region, and the resulting slope-bound problem reduces to linear programming. The framework yields the exact power-efficiency frontier within this model and gives closed-form constraints for representative dissipation exponents, including the maximum-power limit.

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cond-mat.stat-mech 2026-05-05 2 theorems

Thermodynamic relation gives lattice diffusion from ideal case and covariance

A general thermodynamic approach for diffusion on a lattice

The Onsager matrix follows from ideal transport adjusted by the determinant of occupation fluctuations.

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This work presents a general thermodynamic approach to describe particle diffusion on a lattice, a model used to study transport processes in solids and on surfaces. By treating each lattice site as an open thermodynamic system, the effects of microscopic particle interactions are represented through the chemical potential. A fundamental relationship between the Onsager matrix ($L$) and its ideal-system counterpart ($L_\text{id}$, where interactions are neglected) using the determinant of the covariance matrix is demonstrated. This framework allows for the calculation of transport coefficients using the combination of their ideal values and thermodynamic properties. The general result is successfully applied to reproduce the Darken equation for substitutional diffusion in solids and to derive the non-diagonal diffusion matrix of the Zhdanov model for surface diffusion of Langmuir particles. In the last case, analytical predictions are further validated through numerical simulations across various interaction potentials.

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cond-mat.stat-mech 2026-05-05 3 theorems

Motility restores order in active oscillator systems

Topological defects in out-of-equilibrium systems

Allowing oscillators to move triggers a Berezinskii-Kosterlitz-Thouless transition that binds defects despite frequency differences.

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In this PhD thesis, we study topological defects in two-dimensional non-equilibrium systems, focusing on active extensions of the XY model, including activity, mobility and non-reciprocity. In a noisy Kuramoto lattice with short-range coupling, intrinsic frequency heterogeneity destroys quasi-long-range order and fragments the system into finite domains. Defects unbind at all temperatures and exhibit superdiffusive random walks, advected by evolving domain boundaries. By contrast, when oscillators are allowed to move in space, the system undergoes a Berezinskii-Kosterlitz-Thouless transition and regains quasi-long-range order, revealing the fundamental role of motility in sustaining coherence. We also analyse a non-reciprocal O(2) model with vision-cone couplings and derive a continuum theory that captures the same large-scale physics. Non-reciprocity selects defect shapes, enriches the annihilation process, and reshapes patterns through advection. Together, these results elucidate the fundamental role of activity and non-reciprocity in shaping topological defects and ordering in non-equilibrium systems. Keywords: Topological defects, XY model, Steep XY model, Kuramoto model, Non-reciprocal interactions, Active matter, Phase transitions, Berezinskii-Kosterlitz-Thouless transition, Non-equilibrium statistical mechanics

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cond-mat.stat-mech 2026-05-05 3 theorems

Noise broadens SiC MOSFET burnout threshold to probabilistic band

Stochastic first-passage modeling of single-event burnout in SiC power MOSFETs

Stochastic carrier and heat fluctuations create a range of uncertain outcomes and allow rare failures below the nominal threshold.

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Single-event burnout (SEB) in silicon carbide (SiC) power MOSFETs is often characterized by deterministic threshold quantities. Near the boundary between recovery and runaway, stochastic variability can make this threshold description probabilistic rather than sharp. This work introduces a first-passage perspective for stochastic threshold broadening in burnout. The process is described by a reduced electrothermal feedback-relaxation model with an absorbing boundary. The model combines carrier multiplication, avalanche feedback, localized heating, carrier loss, and thermal relaxation. Stochastic carrier and thermal terms represent unresolved event-level variability. The main finding is that finite fluctuations broaden the deterministic burnout threshold into a probabilistic transition band. Noise-induced subthreshold runaway also emerges, where nominally recoverable conditions can still fail through rare stochastic excursions. First-passage-time distributions resolve the time scale of burnout and survival probabilities further distinguish rapid feedback-dominated runaway from delayed stochastic failure. A feedback-relaxation phase diagram organizes recoverable, probabilistic, and rapidly unstable regimes. This framework provides a statistical-physics interpretation of threshold dispersion in single-event burnout of SiC power MOSFETs by linking coarse-grained electrothermal dynamics to probabilistic and time-resolved failure observables.

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cond-mat.stat-mech 2026-05-05 4 theorems

Record ages split into geometry and memory regimes

Aging Record Statistics in Saturating Self-Interacting Random Walks

Exact asymptotics for saturating self-interacting walks show short-time control by explored-region shape and long-time prefactor corrections

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The record age tau_k, defined as the time between the k-th and k+1-st record-breaking events, is a central observable of extreme-value statistics. In Markovian processes, the absence of memory makes tau_k independent of k. How memory breaks this invariance and induces aging, meaning a dependence of tau_k on k, remains a fundamental question, closely connected to widely observed aging phenomena in non-Markovian dynamics. In this Letter, we derive the exact asymptotic distribution of tau_k for saturating self-interacting random walks, a broad class of non-Markovian processes. We uncover two asymptotic regimes, in agreement with recent scaling predictions: at short times (tau much smaller than k squared), record statistics are governed by the geometry of the explored region, while at long times (tau much larger than k squared), memory effects become subdominant and reduce to nontrivial prefactor corrections. Our exact result provides a rare analytic window beyond scaling theory and extends to a framework that fully quantifies aging dynamics in the presence of saturating self-interaction.

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cond-mat.stat-mech 2026-05-05 3 theorems

Wilson loops signal confinement via area laws on the lattice

Lattice Gauge Theory and Wilson-Loop Confinement: A Statistical-Mechanical Survey

Statistical mechanics of gauge ensembles shows closed paths distinguish confined phases through exponential area decay.

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Wilson loops provide the central gauge-invariant probe of confinement in lattice gauge theory. This survey reviews the statistical-mechanical formulation of lattice gauge ensembles, the strong-coupling and duality mechanisms behind area laws, finite-temperature and continuum scaling diagnostics, and the mathematical status of Wilson-loop confinement.

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cond-mat.stat-mech 2026-05-05 3 theorems

Anisotropic mobility drives sub-Gaussian positions in trapped swimmers

Mobility Anisotropy Reshapes Self-Propelled Motion

Exact fourth-moment calculation yields negative kurtosis that varies non-monotonically and displaces the particle outside the expected high-

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We exactly solve the nonequilibrium dynamics of a harmonically trapped self-propelled particle with anisotropic translational mobility in two dimensions, relevant to rodlike microswimmers and wheeled robots. The mean displacement and MSD reveal a quasi-steady plateau with vanishing fluctuations in the high-persistence regime. An exact calculation of steady-state fourth moment yields a negative excess kurtosis that varies non-monotonically with the ratio of mechanical to rotational relaxation timescales. This gives rise to a strictly sub-Gaussian steady-state position distribution, in which the particle with anisotropic mobility, in high persistence regime, is displaced into the high-potential region lying outside the stationary contour set by the activity and harmonic confinement. This is further corroborated by the relaxation of the MSD from the quasi-steady plateau to the steady-state regime.

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cond-mat.stat-mech 2026-05-04 3 theorems

Kicked spin chains show ergodic or time-crystal phases by initial state

Ergodic and Discrete Time Crystal Phases in Periodically Kicked Many-Body Quantum Systems: An Analytical Study

Same kicking strengths produce infinite-temperature relaxation or persistent subharmonic oscillations depending on starting conditions.

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We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the observables. Our derivation explains the criteria and the mechanism that lead to the infinite-temperature statistical average of observables at long times, irrespective of the initial state. When the criteria are violated, the observables oscillate with time. These oscillations are subharmonic and robust to small perturbations, suggesting the emergence of a discrete time crystal phase. We demonstrate these features explicitly in periodically kicked nonintegrable spin chains. For a spin chain with two kicks per cycle, we show that the kicked chain can exhibit an ergodic or a discrete-time crystal phase for the same kicking strengths, depending on the initial state preparation. We complement our time-evolution study of observables with the spectral form factor of these kicked models.

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cond-mat.stat-mech 2026-05-04

Point contacts restrict high-dimensional systems to weak coupling only

System driven out-of equilibrium by weak contacts with reservoirs

Mesoscopic contacts restore macroscopic fluctuation theory and permit an extended additivity principle for multiple reservoirs.

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The non-equilibrium behavior of particle systems driven by reservoirs has been extensively studied in recent years. In one dimension, various regimes have been explored depending on the coupling strength to the reservoirs. In this paper, we investigate the role of the dimension and of the geometry of the contacts with the reservoirs. For the symmetric simple exclusion process with point contact reservoirs, we show that in dimension 2, as in one dimension, three different regimes occur depending on the coupling strength. On the other hand in dimensions 3 and higher, there exists only a weak coupling regime which is very sensitive to the microscopic structure of the contacts. We then argue that for reservoirs with mesoscopic size contacts the macroscopic fluctuation theory remains in force and we propose an extension of the additivity principle for multiple mesoscopic reservoirs.

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cond-mat.stat-mech 2026-05-04

Percolation model uncovers hidden nuclear reactor hazards

Directed percolation in nuclear safety

Treating neutron generations as a directed percolation process reveals safety risks that standard systems miss in some cases.

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Neutron behavior in a nuclear reactor is described using a directed percolation model. The preferred direction is created by generations of neutrons oriented in time. Using the example of the time it takes for a dangerous neutron flux or reactor power limit to be reached, it is shown that in certain situations, the proposed approach can identify events hazardous to reactor safety that are undetectable by traditional reactor safety systems.

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cond-mat.stat-mech 2026-05-04 3 theorems

XXZ spin conductivity scales as 1/T at high temperature

Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

The proportionality constant diverges when one-quasiparticle magnetization is infinite due to 1/N-scaled long-range correlations.

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Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.

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cond-mat.stat-mech 2026-05-04 3 theorems

Researchers analyzed EEG amplitude distributions from typical and ADHD children using…

Brain criticality through nonadditive entropic analysis of electroencephalograms

EEG amplitudes follow q-Gaussian distributions where the entropic index q varies monotonically with β, revealing critical brain behavior…

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On the grounds of nonadditive entropies -- appropriate for complex systems -- we investigate the electroencephalogram amplitudes of typical and ADHD children. The corresponding probability distributions are $q$-Gaussians, i.e., $\rho(x) \propto e_q^{-\beta x^2} \equiv [1+(q-1) \beta x^2]^{1/(1-q)}$, where $(q,\beta)$ are, respectively, the entropic index characterizing complexity and the inverse width. We show that $q$ tends to monotonically vary with $\beta$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path. We show that $q$ tends to monotonically vary with $\beta$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path.

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cond-mat.stat-mech 2026-05-04 2 theorems

Logarithmic method recovers adiabatic scaling in excitable systems

Breakdown of Adiabatic Scaling and Noise-Induced Functional Synchronization in Deeply Quiescent Excitable Systems

It cuts through jitter to reveal optimal noise levels and a transition from shivering to functional synchronization in coupled cells.

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Coherence resonance (CR) characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we investigate the stochastic dynamics of a 3D Sherman-Rinzel-Keizer (SRK) model driven by multiplicative Feller noise. We show that traditional extremal evaluations of CR encounter a "bathtub effect" a broad resonance valley that can lead to statistical inaccuracies. To address this, we propose a logarithmic centroid extraction method, which filters out stochastic jitter and recovers the underlying adiabatic Kramers scaling with high linearity (R^2 > 0.95). Furthermore, we identify the physical boundary where this adiabatic approximation breaks down under the strong-noise limit. Extending our analysis to gap-junction coupled systems, we observe a noise-induced transition from sub-threshold physiological shivering (characterized by statistical correlation but negligible functional output) to macroscopic functional synchronization. Our results provide a mathematical framework for extracting optimal noise intensities in broad energy valleys and offer insights into how quiescent biological systems utilize stochastic fluctuations for functional recovery

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cond-mat.stat-mech 2026-05-04

Transmission at interfaces sets long-time entanglement growth

Entanglement dynamics after quenches with inhomogeneous Hamiltonians

After quenches with left-right inhomogeneous Hamiltonians, the analytically derived transmission coefficient controls how entanglement and a

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We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schr\"odinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.

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cond-mat.stat-mech 2026-05-04

Repulsive run-and-tumble particles gain effective attractions

Microscopic theory of soft run-and-tumble particles

An iterative expansion in interaction couplings derives the two-point correlations that characterize their stationary state.

abstract click to expand

Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large self-propulsion. Complementing a companion paper that characterises effective attraction between two soft run-and-tumble particles [Garcia-Millan et al., Effective attraction by repulsion (2026)], here we provide a thorough derivation of our microscopic theory, which is an exact representation of the particle dynamics. We report the systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings, by adding, order by order, loop corrections. We use the effective interaction vertices to calculate the two-point correlation function, fully characterising the stationary state. Other observables, such as the structure factor, overlap probability and entropy production rate are calculated as well.

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cond-mat.stat-mech 2026-05-04

Repulsion yields higher-order attraction in run-and-tumble particles

Effective attraction by repulsion

Exact two-particle theory shows leading repulsion but attractive corrections that can drive clustering.

abstract click to expand

Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between particles. Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective repulsion, while effective attraction emerges as a higher-order contribution to the renormalisation of the pair potential.

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