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Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media

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Pith's one-line read These lecture notes argue that in d>1 the optimal trajectory for a current fluctuation carries a mobility-weighted, curl-free structure (Eq.

desk verdict A clear, honest lecture-note synthesis of current large deviation theory, with a speculative packing-field proposal; the real caveat is the unproven single-principal-direction ansatz, not the flagged C^2 regularity issue. read the letter →

arxiv 2501.09629 v1 pith:6DEXTRMP submitted 2025-01-16 cond-mat.stat-mech cond-mat.softmath-phmath.MPnlin.PSphysics.flu-dyn

Pablo I. Hurtado This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.softmath-phmath.MPnlin.PSphysics.flu-dyn
keywords largedeviationsmacroscopicfluctuationtheoryadditivityprinciplecurrentfluctuationsdynamicalphasetransitionstravelingwavestimecrystalsDoobtransform
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

These lecture notes argue that the variational path sustaining a rare current fluctuation changes character when the system has more than one spatial dimension. In d>1, the optimal current vector field is forced by a mobility-weighted curl-free condition to develop structure in every component transverse to the driving direction, with that structure tied nonlocally to the mobility of the entire optimal density profile. Because a structured current field never costs more than a uniform one whenever the current has transverse components, the weak additivity principle strictly dominates the strong additivity principle. The notes also develop a unified picture of dynamical phase transitions: discrete particle-hole symmetry breaking in open channels and continuous time-translation breaking by traveling waves in periodic systems, both traced to an emergent degeneracy of the leading eigenspace of the biased generator. If correct, these results set the architecture that any theory or simulation of current fluctuations in d>1 must respect.

What carries the argument

The load-bearing object is the reduced optimal excess current $\chi_q\equiv [j_q+D_q\nabla\rho_q-\sigma_q E]/\sigma_q$, whose Jacobian equals the Hessian of the Lagrange-multiplier field $\psi_q$; Schwarz's theorem makes that Hessian symmetric when $\psi_q$ is $C^2$, and the symmetry propagates to the mobility-weighted curl-free condition $\partial_\beta(j_{\alpha,q}/\sigma_q)=\partial_\alpha(j_{\beta,q}/\sigma_q)$ on the optimal current field. The second piece of machinery is the weak additivity principle, which assumes time-independent optimal paths with structure along one principal direction, a divergence-free current, and the nonlocal transverse-current formula (45) or (46). A comparison via the reverse Hölder inequality shows the weak-additivity functional always dominates the strong-additivity functional by $\Delta F_q=\frac{q_\perp^2}{2}[\int dx\,\sigma^{-1}-(\int dx\,\sigma)^{-1}]\geq 0$. The spectral machinery is the tilted or Doob-transformed generator: dynamical phase transitions appear as a closing of the spectral gap, with phase probability vectors built from the subleading eigenvectors of the degenerate leading eigenspace.

What would settle it

Take a d>1 driven diffusive model with density-dependent mobility (for example, two-dimensional WASEP or KMP on a ring with a current bias), compute the optimal trajectory numerically by action minimization or rare-event cloning, and measure the orthogonal current component $j_{\perp,q}(x_\parallel)$ along the optimal path. If $j_{\perp,q}(x_\parallel)$ is not proportional to $\sigma[\rho_q(x_\parallel)]$ with the global normalization of Eq. (45), or if the Jacobian of $\chi_q$ is not symmetric, the central theorem fails. A sharper test is to construct a regime with a known singular $\psi_q$—for instance a boundary or constraint producing a shock in the multiplier field—and check whether Eq. (43) is violated at the singularity.

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Extended reading notes

Core claim

The central claim is a structural theorem for optimal paths: for any d-dimensional driven diffusive system described by macroscopic fluctuation theory, the optimal current field $j_q(r,t)$ of a fluctuation $q$ satisfies $\partial_\beta(j_{\alpha,q}/\sigma_q)=\partial_\alpha(j_{\beta,q}/\sigma_q)$ for all $\alpha,\beta$ (Eq. 43), provided the optimal Lagrange-multiplier field $\psi_q$ is twice continuously differentiable. For optimal paths with structure along one principal direction, this forces every orthogonal component to take the nonlocal form $j_{\beta,q}(x_\parallel,t)=q_\beta\,\tau\,\sigma[\rho_q(x_\parallel,t)]/\int_0^\tau ds\int_0^1 dy\,\sigma[\rho_q(y,s)]$ (Eq. 45), so the transverse current is set by the space-time averaged mobility of the whole optimal density profile. Consequently, the correct d>1 extension of the additivity principle is the weak version, in which the optimal current is divergence-free and structured, and this strictly dominates the strong version whenever $q_\perp\neq 0$ and the mobility depends on density. The notes further establish that the dynamical phase transitions seen in these systems—Z2 particle-hole symmetry breaking in open channels and traveling-wave/time-crystal phases in periodic rings—share a common spectral origin: an emergent degeneracy of the leading eigenspace of the tilted generator, with the subleading eigenvectors carrying the symmetry-breaking structure.

Load-bearing premise

Everything rests on the optimal Lagrange-multiplier field $\psi_q$ being twice continuously differentiable in space so that its Hessian is symmetric; if some driven system realizes a singular $\psi_q$, the claimed mobility-weighted curl-free architecture of optimal currents can fail.

Editorial extensions

If this is right

  • For any d>1 driven diffusive system, the current large-deviation function must be computed from structured optimal current fields; the strong additivity principle is strictly suboptimal whenever the current has transverse components and the mobility depends on density.
  • During a fluctuation, every component of the optimal current orthogonal to the principal direction is slaved to the whole optimal density profile through Eq. (45), making current statistics in d>1 spatiotemporally nonlocal.
  • For currents with no transverse component, $q_\perp=0$, the weak and strong additivity principles coincide, which reconciles apparently conflicting earlier results on the validity of additivity in higher dimensions.
  • Open and periodic driven systems both exhibit dynamical phase transitions at the fluctuation level: Z2 particle-hole symmetry breaking in open channels, and traveling-wave phases that break continuous time-translation symmetry in rings.
  • The microscopic signature of these transitions is an emergent degeneracy of the leading eigenspace of the tilted generator; in the traveling-wave case the degenerate eigenvalues form a band with constant imaginary spacing, giving time-crystal order that the Doob/packing-field mechanism can make programmable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct but unstated corollary is that rare-event simulation and path-contraction schemes in d>1 that parameterize optimal paths by spatially uniform currents are systematically biased away from the true minimizer; optimal biasing protocols should propose divergence-free structured currents of the mobility-weighted nonlocal form.
  • The same mobility-weighted curl-free argument should extend to fluctuations of several coupled conserved currents, where the optimal vector field of each current would be coupled to the mobility tensor of the whole set; this is a natural generalization the notes do not spell out.
  • The regularity caveat on $\psi_q$ identifies a testable boundary: models with hard constraints, shocks, or singular optimal density profiles may realize the singular-$\psi_q$ case, and in those models the claim that weak additivity always dominates strong additivity could fail.
  • The packing-field route to time crystals suggests experimental feedback protocols for colloidal or active-matter systems, where configuration-dependent fields can be imposed in real time; the notes only sketch this as a future direction.
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Formalized claims in Lean

  1. Claim #1: The central claim is a structural theorem for optimal paths: for any d-dimensional driven diffusive system described by macroscopic fluctuation theory, the optimal current field $j_q(r,t)$ of a fluctuation $q$ satisfies $\partial_\beta(j_{\alpha,q}/\sigma_q)=\partial_\alpha(j_{\beta,q}/\sigma_q)$ for all $\alpha,\beta$ (Eq. 43), provided the optimal Lagrange-multiplier field $\psi_q$ is twice cont

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. These lecture notes use macroscopic fluctuation theory and microscopic spectral methods to analyze large deviations of the time-averaged current in driven diffusive systems. After reviewing the 1d additivity principle, the author derives a symmetry constraint (Eq. 43) on the optimal current vector field in d>1, uses it to formulate the weak additivity principle with nonlocal orthogonal current components (Eqs. 45-49), and proves that this wAP dominates the strong additivity principle. The notes then analyze a Z2 symmetry-breaking dynamical phase transition in open particle-hole-symmetric systems via a Landau-like theory and joint mass-current LDF, conjecturing an instanton/Maxwell construction in the non-convex regime. They analyze a time-translation-breaking DPT in periodic systems (traveling waves), connect it to spectral degeneracies of the tilted/Doob generator, and propose a packing-field mechanism for programmable time crystals. Conjectural steps are explicitly flagged.

Significance. The central claim that current fluctuations in d>1 are carried by structured, mobility-coupled nonlocal current fields, rather than uniform ones, is important and, if correct, changes how current LDFs should be computed in higher dimensions. The proof that wAP dominates sAP (Eq. 52) is clean and the derivation of the critical thresholds in the stability analyses is internally consistent. The lecture notes are pedagogically valuable and unusually transparent: the C²-smoothness limitation on ψ_q and the conjectural status of the instanton (Section 4.4) and the traveling-wave ansatz (Section 5.2) are acknowledged. The spectral viewpoint of Section 6 provides a concrete microscopic mechanism for DPTs and leads to falsifiable predictions for programmable time crystals via the packing field of Section 7, which is a strength of the manuscript.

major comments (2)
  1. [§3.1, Eq. (45)] The derivation of Eq. (45) is presented as a consequence of Eq. (43), which holds only if the optimal multiplier ψ_q is twice continuously differentiable; the text itself acknowledges that singular ψ_q could violate Eq. (43). Because Eq. (45) is the quantitative core of the weak additivity principle, this smoothness assumption is load-bearing as written. The gap can be closed by deriving Eq. (45) directly from the variational equation (36) and the single-direction ansatz (44): under that ansatz the transverse component of Eq. (36) implies that j⊥,q/σq is constant, and the empirical-current constraint fixes that constant to q⊥/(τ^{-1}∫∫σ). The manuscript should present this direct route, or prove C² regularity, and remove the implication that the nonlocal structure of Eq. (45) rests on Schwarz's theorem.
  2. [§3.1–3.2, Eqs. (44) and (49)] The wAP functional (49) and the dominance result (52) are derived under the ansatz that optimal fields have structure along a single principal direction and, for the wAP itself, are time-independent. This ansatz is asserted as 'typical' rather than derived. If the true MFT optimum develops genuine d-dimensional transverse structure or time dependence not captured by Eq. (44), then Eq. (45) and the wAP functional are not exact variational bounds. This is a load-bearing assumption for the central claim that wAP is the relevant simplifying principle in d>1. The manuscript should state this limitation wherever Eq. (45) is used and ideally provide a concrete test, for example by checking transverse gradients of the optimal density and current fields in the 2D simulations cited after Eq. (49).
minor comments (5)
  1. [§3, opening paragraph] The word 'Aditivity' appears as a typo for 'additivity', and similar typos occur throughout ('excersise' near Eq. (14), 'constat' near Eq. (24), 'precission' in §3.3, 'assymetric' in §6.7).
  2. [§5.1, after Eq. (115)] The phrase 'to simplify the calculation the calculation' contains a duplicated word and should be corrected.
  3. [Fig. 6 caption] The caption reads 'eigenvertors' where 'eigenvectors' is intended; please correct this and similar spelling errors in the figure captions.
  4. [§7.2, Eq. (174)] The numerical coefficient 1/10 in Eq. (174) is introduced from a fit to WASEP data at specific parameters, yet the text calls the expression 'quite generically'; either qualify this coefficient as model-dependent or provide a derivation.
  5. [§7.4, after Eq. (186)] The jump from the linear instability threshold (Eq. (186)) to the claim of rotating multi-condensate states for all η>η_c^{(m)} goes beyond linear theory; the numerical solutions of Eq. (179) support the claim, but the text should explicitly mark this as a conjecture for the nonlinear regime.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the d>1 optimal-current architecture is derived from the MFT variational equations and the explicitly stated principal-direction ansatz, not assumed from the target LDF.

full rationale

The derivation chain is self-contained. The current LDF is defined through the MFT action (Eq. 28), and the variational equations (35)-(36) are obtained by functional differentiation. Eq. (43) follows from the symmetry of the Hessian of the Lagrange-multiplier field ψ_q via Schwarz's theorem, a mathematical consequence of the Euler-Lagrange equation (36), not an input assumption. Eq. (45) follows from Eq. (43) together with the explicitly stated single-principal-direction ansatz (44) and the empirical-current constraint; it is a derived consequence, not a fitted or renamed input. The wAP-vs-sAP comparison is a direct reverse-Hölder inequality (Eqs. 52-53), independent of any fitted data. The self-citations to refs. [27,50,52,53,71,101-103] are used for prior context and for independent simulation/exact checks, and the notes re-derive the central results rather than importing them as black boxes. The C^2 regularity caveat for ψ_q and the principal-direction ansatz are validity/assumption risks, not circular reductions; a failure of these assumptions would make Eq. (43)/(45) inapplicable, but would not make the derivation equivalent to its inputs.

Assumptions & free parameters 2 free parameters · 6 assumptions · 2 invented entities

The paper rests on the MFT weak-noise approximation, the additivity conjecture, and several ad hoc ansatze (traveling wave, packing field). Most numerical confirmations are cited from the author's earlier work rather than reproduced here. The only fitted quantity used in a constructive way is the 1/10 coefficient in the Doob smart field.

free parameters (2)
  • η (packing field coupling) = control parameter, not fitted
    In §7.3-7.4 the TCLG model sets E_k(C)=ε+ηE_k^{(m)}(C); η is a free coupling constant, and the critical value η_c^{(m)}=4πm D̄ ρ̄ /σ̄ is derived, so η itself is not fitted to data.
  • coefficient 1/10 in g_{λ,L}(r) = 1/10
    In §7.2, the function g_{λ,L}(r)≡f'/f is 'empirically found' to be ≈ -λ L r/10, and this fit is used to write the Doob smart field as Eq (174). This is a fitted coefficient in a numerical observation.
assumptions (6)
  • domain assumption MFT action (weak-noise Gaussian field theory with local equilibrium)
    Eqs (3)-(7) assume a fluctuating hydrodynamic description with Gaussian white noise and local equilibrium transport coefficients; all subsequent LDF calculations rest on it.
  • domain assumption Additivity principle (time-independent optimal path)
    The 1d current LDF is computed under the additivity conjecture of Bodineau-Derrida, which is an assumption, as explicitly stated in §2.1; violations are later shown in §4.4.
  • ad hoc to paper C2 smoothness of ψ_q
    Derivation of the fundamental relation (43) requires Hessian symmetry of ψ_q, i.e. ψ_q ∈ C2; the paper itself flags singular ψ_q as a possible exception.
  • ad hoc to paper Traveling wave ansatz beyond the instability
    In §5.2 the optimal fields in the symmetry-broken phase are assumed to be of the form ρ=ω(x-vt); this ansatz is conjectured and not derived from the MFT action.
  • ad hoc to paper Packing-field ansatz for programmable time crystals
    The TCLG model and the hydrodynamic equation (179)-(180) with packing field E_x^{(m)}[ρ] are introduced as a mechanism, motivated by the Doob smart field but not derived uniquely from it.
  • standard math Perron-Frobenius and spectral decomposition of the tilted generator
    Section 6 relies on the Perron-Frobenius theorem and the biorthogonal spectral decomposition of the tilted generator, standard results in Markov chain theory.
invented entities (2)
  • Packing field E_k^{(m)}(C) (and hydrodynamic E_x^{(m)}[ρ]) independent evidence
    purpose: Configuration-dependent external field that amplifies the m-th Fourier mode of density to stabilize m rotating condensates, enabling programmable time crystals.
    It makes falsifiable predictions: the critical coupling (186), traveling-wave speed ω=2πm σ̄' ε, number of condensates m, and the scaling ρ_m(ω_m t - 2πm x)=ρ_1(mω_1 t - 2πm x). These can be tested numerically and in proposed colloidal ring experiments (§7.4).
  • Time-crystal lattice gas (TCLG) model independent evidence
    purpose: A variant of WASEP with a packing field to study time-crystal phases.
    The model is defined with clear parameters and the hydrodynamic limit is derived, giving quantitative predictions for simulations and experiments.

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Pith. "Pith review of Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media." pith.science (2026). https://pith.science/paper/6DEXTRMP

@misc{pith2026250109629,
  author       = {Pith},
  title        = {Pith review of: Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6DEXTRMP}},
  note         = {Machine review of arXiv:2501.09629}
}
read the original abstract

Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation statistics of the current, a central observable out of equilibrium, using mostly macroscopic fluctuation theory (MFT) but also microscopic spectral methods. Special emphasis is put on describing the optimal path leading to a rare fluctuation, as well as on different dynamical symmetry breaking phenomena that appear at the fluctuating level. We start with an overview of trajectory statistics in driven diffusive systems as described by MFT. We discuss the additivity principle, a simplifying conjecture to compute the current distribution in one-dimensional nonequilibrium systems, and extend this idea to higher dimensions, where the nonlocal structure of the optimal current vector field becomes crucial. Next we explore dynamical phase transitions (DPTs) in current fluctuations, which manifest as symmetry-breaking events in trajectory statistics. These include particle-hole symmetry-breaking DPTs in open channels, for which we work out a Landau-like theory as well as the joint statistics of the current and the order parameter. Time-translation symmetry-breaking DPTs in periodic systems are also discussed, where coherent traveling condensates emerge to facilitate current deviations. We also discuss the microscopic spectral mechanism leading to these DPTs, which is linked to an emerging degeneracy of the leading eigenspace. Using this spectral perspective, we find the signatures of the recently discovered time-crystal phases of matter in traveling-wave DPTs, and use Doob's transform to propose a packing-field mechanism to create programmable time-crystals in driven systems. Finally, we address open challenges and future directions in this rapidly evolving field.

Figures

Figures reproduced from arXiv: 2501.09629 by the authors.

Figure 1
Figure 1. An interesting problem. Top panel: A channel of length L connects two reservoirs at different densities. Particles might be also driven in some preferential direction by an external field E. Due to the density gradient, a particle current ensues. Bottom left panel: Different realizations of the experiment for long but finite time τ lead to different values of the cumulative current Qτ and hence to a distribution of … view at source ↗
Figure 2
Figure 2. Dynamical symmetry breaking in open systems. (a) Mobility σ(ρ) = ρ(1 − ρ) for the WASEP model of particle diffusion under exclusion interactions. Note the particle-hole symmetry σ(ρ) = σ(1 − ρ) of this transport coefficient. For equal boundary densities, ρ0 = 1 2 = ρ1 , the optimal density profile ρq (x) for mild current fluctuations around the average current 〈q〉 is just homogeneous, ρq (x) = 1 2 , see panel (b), a… view at source ↗
Figure 3
Figure 3. Landau-like theory for the DPT in open systems. Typical shape of the function G(δm|q) of Eq. (95) as a function of the excess mass δm and the current q for the case (a) when σ¯ ′′ > 0 and g4 > 0 and (b) when σ¯ ′′ < 0 and g4 > 0. In case (a) two equivalent minima appear in G(δm|q) at excess masses ±δmq ̸= 0 for |q| > qc , see Eq. (96), while in (b) these two equivalent minima appear for |q| < qc . q 2 > q 2 c (SSB p… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Joint mass-current fluctuations for the 1d open WASEP. (a) Total mass LDF conditioned on a given current, G(m|q) = G(q) − G(m, q), as a function of the mass m for different currents q, for equal and PH-symmetric boundary densities, ρ0 = 0.5 = ρ1 , and external field E …
Figure 5
Figure 5. Figure 5: Time-translation symmetry breaking in 1d periodic systems. Typical evolution of microscopic configurations for current fluctuations q above and below the critical threshold, and shape of the optimal density field as a function of q, for two different transport models o…
Figure 6
Figure 6. Figure 6: A spectral view on dynamical criticality for the 1d open WASEP. (a) Sketch of the 1d boundary-driven WASEP, where N particles in a lattice of L sites jump randomly to empty neighboring sites with asymmetric rates p±. (b) Scaled spectral gaps, L 2∆λ j , as a function of…
Figure 7
Figure 7. Figure 7: Dynamical phase transition for the 1d periodic WASEP. (a) Sketch of the WASEP model in a 1d periodic lattice, with stochastic particle jumps to neighboring empty sites at rates p±. The total number of particles is conserved. (b) Magnitude of the packing order parameter…
Figure 8
Figure 8. Figure 8: Spectral signatures of the time-crystal phase for the 1d periodic WASEP and packing field. (a)-(d) Structure in the complex plane of the leading scaled spec￾tral gaps L 2∆λ j with ρ¯ = 1/3, E = 10 > Ec , and lattice sizes L = 9, 12, 15, 18, 21, 24 for (a) the homogeneo…
Figure 9
Figure 9. Figure 9: Programmable time crystals from higher-order packing fields. (a)-(b) Coupling a many-body particle system to an mth-order packing field E (m) (C) with strength η beyond a critical threshold can trigger an instability to a time-crystal phase characterized by the formati…

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Works this paper leans on

187 extracted references · 70 canonical work pages · cited by 1 Pith paper

  1. [1]

    Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, J

    B. Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, J. Stat. Mech. P07023 (2007)

    2007

  2. [2]

    Bertini, A

    L. Bertini, A. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctua- tion theory, Rev. Mod. Phys. 87(2), 593 (2015)

    2015

  3. [3]

    Livi and P

    R. Livi and P . Politi,Nonequilibrium Statistical Physics: A Modern Perspective, Cambridge University Press, doi:10.1017 /9781107278974 (2017)

    2017

  4. [4]

    Marro and R

    J. Marro and R. Dickman,Nonequilibrium phase transitions in lattice models, Cambridge University Press (2005)

    2005

  5. [5]

    De Groot and P

    S. De Groot and P . Mazur,Non-Equilibrium Thermodynamics, Dover Books on Physics. Dover Publications, New York, ISBN 9780486153506 (2013)

    2013

  6. [6]

    Peliti and S

    L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction , Princeton Uni- versity Press, ISBN 9780691201771 (2021)

    2021

  7. [7]

    Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines , Rep

    U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines , Rep. Prog. Phys. 75(12), 126001 (2012)

    2012

  8. [8]

    Touchette, The large deviation approach to statistical mechanics, Phys

    H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478(1-3), 1 (2009)

    2009

Show all 187 references
  1. [9]

    Gallavotti and E

    G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett. 74(14), 2694 (1995). 63 SciPost Physics Lecture Notes Submission

    1995

  2. [10]

    Gallavotti and E

    G. Gallavotti and E. G. D. Cohen,Dynamical ensembles in stationary states, J. Stat. Phys. 80(5-6), 931 (1995)

    1995

  3. [11]

    Kurchan, Fluctuation theorem for stochastic dynamics, J

    J. Kurchan, Fluctuation theorem for stochastic dynamics, J. Phys. A31(16), 3719 (1998)

    1998

  4. [12]

    J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, J. Stat. Phys. 95(1-2), 333 (1999)

    1999

  5. [13]

    Andrieux and P

    D. Andrieux and P . Gaspard,A fluctuation theorem for currents and non-linear response coefficients, J. Stat. Mech. P02006 (2007)

    2007

  6. [14]

    P . I. Hurtado and P . L. Garrido,Spontaneous symmetry breaking at the fluctuating level, Phys. Rev. Lett.107(18), 180601 (2011)

    2011

  7. [15]

    Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys

    C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys. Rev. E 56(5), 5018 (1997)

    1997

  8. [16]

    Jarzynski, Nonequilibrium equality for free energy differences, Phys

    C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett.78(14), 2690 (1997)

    1997

  9. [17]

    Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J

    G. Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys. 90(5-6), 1481 (1998)

    1998

  10. [18]

    G. E. Crooks, Path-ensemble averages in systems driven far from equilibrium, Phys. Rev. E 61(3), 2361 (2000)

    2000

  11. [19]

    Hatano and S

    T . Hatano and S. Sasa,Steady-state thermodynamics of Langevin systems, Phys. Rev. Lett. 86(16), 3463 (2001)

    2001

  12. [20]

    Bertini, D

    L. Bertini, D. Gabrielli, G. Jona-Lasinio and C. Landim,Thermodynamic transformations of nonequilibrium states, J. Stat. Phys. 149(5), 773 (2012)

    2012

  13. [21]

    Bertini, D

    L. Bertini, D. Gabrielli, G. Jona-Lasinio and C. Landim,Clausius inequality and optimal- ity of quasistatic transformations for nonequilibrium stationary states , Phys. Rev. Lett. 110(2), 020601 (2013)

    2013

  14. [22]

    A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular pro- cesses, Phys. Rev. Lett. 114(15), 158101 (2015)

    2015

  15. [23]

    T . R. Gingrich, J. M. Horowitz, N. Perunov and J. L. England, Dissipation bounds all steady-state current fluctuations, Phys. Rev. Lett. 116(12), 120601 (2016)

    2016

  16. [24]

    Pietzonka and U

    P . Pietzonka and U. Seifert, Universal trade-off between power, efficiency, and constancy in steady-state heat engines , Phys. Rev. Lett. 120, 190602 (2018), doi:10.1103/PhysRevLett.120.190602

    2018 doi

  17. [25]

    J. M. Horowitz and T . R. Gingrich,Thermodynamic uncertainty relations constrain non- equilibrium fluctuations, Nature Physics 16(1), 15 (2020), doi:10.1038 /s41567-019- 0702-6

    2020

  18. [26]

    Bertini, A

    L. Bertini, A. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Fluctuations in stationary nonequilibrium states of irreversible processes, Phys. Rev. Lett. 87(4), 040601 (2001)

    2001

  19. [27]

    Bodineau and B

    T . Bodineau and B. Derrida,Current fluctuations in nonequilibrium diffusive systems: An additivity principle, Phys. Rev. Lett. 92(18), 180601 (2004). 64 SciPost Physics Lecture Notes Submission

    2004

  20. [28]

    Bertini, A

    L. Bertini, A. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Current fluctuations in stochastic lattice gases, Phys. Rev. Lett. 94(3), 030601 (2005)

    2005

  21. [29]

    Bodineau and B

    T . Bodineau and B. Derrida, Distribution of current in nonequilibrium diffusive systems and phase transitions, Phys. Rev. E 72(6), 066110 (2005)

    2005

  22. [30]

    R. J. Harris, A. Rakos and G. M. Schutz, Current fluctuations in the zero-range process with open boundaries, J. Stat. Mech. p. P08003 (2005)

    2005

  23. [31]

    Giardinà, J

    C. Giardinà, J. Kurchan and L. Peliti,Direct evaluation of large-deviation functions, Phys. Rev. Lett.96(12), 120603 (2006)

    2006

  24. [32]

    Bertini, A

    L. Bertini, A. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim,Stochastic interacting particle systems out of equilibrium, J. Stat. Mech. p. P07014 (2007)

    2007

  25. [33]

    Derezinski, W

    J. Derezinski, W . D. Roeck and C. Maes,Fluctuations of quantum currents and unravelings of master equations, J. Stat. Phys. 131(2), 341 (2008)

    2008

  26. [34]

    Derrida and A

    B. Derrida and A. Gerschenfeld, Current Fluctuations in One Dimensional Diffusive Sys- tems with a Step Initial Density profile, J. Stat. Phys. 137(5-6), 978 (2009)

    2009

  27. [35]

    Derrida and A

    B. Derrida and A. Gerschenfeld, Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial condition, J. Stat. Phys. 136(1), 1 (2009)

    2009

  28. [36]

    P . I. Hurtado and P . L. Garrido,Test of the additivity principle for current fluctuations in a model of heat conduction, Phys. Rev. Lett. 102(25), 250601 (2009)

    2009

  29. [37]

    Gorissen, J

    M. Gorissen, J. Hooyberghs and C. Vanderzande,Density-matrix renormalization-group study of current and activity fluctuations near nonequilibrium phase transitions , Phys. Rev. E79, 020101 (2009), doi:10.1103 /PhysRevE.79.020101

    2009

  30. [38]

    P . I. Hurtado and P . L. Garrido,Large fluctuations of the macroscopic current in diffusive systems: A numerical test of the additivity principle, Phys. Rev. E 81(4), 041102 (2010)

    2010

  31. [39]

    P . L. Krapivsky and B. Meerson,Fluctuations of current in nonstationary diffusive lattice gases, Phys. Rev. E 86(3), 031106 (2012)

    2012

  32. [40]

    Gorissen and C

    M. Gorissen and C. Vanderzande,Current fluctuations in the weakly asymmetric exclusion process with open boundaries, Phys. Rev. E 86(5), 051114 (2012)

    2012

  33. [41]

    Akkermans, T

    E. Akkermans, T . Bodineau, B. Derrida and O. Shpielberg,Universal current fluctuations in the symmetric exclusion process and other diffusive systems , Europhys. Lett. 103(2), 20001 (2013)

    2013

  34. [42]

    Meerson and P

    B. Meerson and P . V . Sasorov,Extreme current fluctuations in a nonstationary stochastic heat flow, J. Stat. Mech. P12011 (2013)

    2013

  35. [43]

    Pérez-Espigares, P

    C. Pérez-Espigares, P . L. Garrido and P . I. Hurtado,Dynamical phase transition for current statistics in a simple driven diffusive system, Phys. Rev. E 87(3), 032115 (2013)

    2013

  36. [44]

    P . I. Hurtado, C. P . Espigares, J. J. del Pozo and P . L. Garrido,Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation, J. Stat. Phys. 154(1-2), 214 (2014)

    2014

  37. [45]

    Meerson and P

    B. Meerson and P . V . Sasorov, Extreme current fluctuations in lattice gases: Beyond nonequilibrium steady states, Phys. Rev. E 89(1), 010101 (2014). 65 SciPost Physics Lecture Notes Submission

    2014

  38. [46]

    Kumar, H

    N. Kumar, H. Soni, S. Ramaswamy and A. K. Sood, Anisotropic isometric fluctuation relations in experiment and theory on a self-propelled rod , Phys. Rev. E 91(3), 030102 (2015)

    2015

  39. [47]

    Lazarescu, The physicist’s companion to current fluctuations: one-dimensional bulk- driven lattice gases, J

    A. Lazarescu, The physicist’s companion to current fluctuations: one-dimensional bulk- driven lattice gases, J. Phys. A 48(50), 503001 (2015)

    2015

  40. [48]

    Mendl and H

    C. Mendl and H. Spohn, Current fluctuations for anharmonic chains in thermal equilib- rium, J. Stat. Mech. P03007 (2015)

    2015

  41. [49]

    Becker, K

    T . Becker, K. Nelissen and B. Cleuren,Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study, New J. Phys. 17, 055023 (2015)

    2015

  42. [50]

    Pérez-Espigares, P

    C. Pérez-Espigares, P . L. Garrido and P . I. Hurtado,Weak additivity principle for current statistics in d-dimensions, Phys. Rev. E 93(4), 040103(R) (2016)

    2016

  43. [51]

    Villavicencio-Sanchez and R

    R. Villavicencio-Sanchez and R. J. Harris, Local structure of current fluctuations in diffu- sive systems beyond one dimension, Phys. Rev. E 93(3), 032134 (2016)

    2016

  44. [52]

    Y. Baek, Y. Kafri and V . Lecomte,Dynamical symmetry breaking and phase transitions in driven diffusive systems, Phys. Rev. Lett. 118, 030604 (2017)

    2017

  45. [53]

    Tizón-Escamilla, P

    N. Tizón-Escamilla, P . I. Hurtado and P . L. Garrido,Structure of the optimal path to a fluctuation, Phys. Rev. E 95, 002100 (2017)

    2017

  46. [54]

    Carollo, J

    F . Carollo, J. P . Garrahan, I. Lesanovsky and C. Pérez-Espigares,Fluctuating hydrodynam- ics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains , Phys. Rev. E96, 052118 (2017), doi:10.1103 /PhysRevE.96.052118

    2017

  47. [55]

    Lazarescu, Generic dynamical phase transition in one-dimensional bulk-driven lattice gases with exclusion, J

    A. Lazarescu, Generic dynamical phase transition in one-dimensional bulk-driven lattice gases with exclusion, J. Phys. A 50(25), 254004 (2017)

    2017

  48. [56]

    Tizón-Escamilla, C

    N. Tizón-Escamilla, C. Pérez-Espigares, P . L. Garrido and P . I. Hurtado, Order and symmetry-breaking in the fluctuations of driven systems , Phys. Rev. Lett. 119, 090602 (2017), doi:10.1103 /PhysRevLett.119.090602

    2017

  49. [57]

    Chleboun, S

    P . Chleboun, S. Grosskinsky and A. Pizzoferrato, Current large deviations for partially asymmetric particle systems on a ring, J. Phys. A 51(40), 405001 (2018)

    2018

  50. [58]

    Carollo, J

    F . Carollo, J. P . Garrahan and I. Lesanovsky , Current fluctuations in boundary-driven quantum spin chains , Phys. Rev. B 98, 094301 (2018), doi:10.1103/PhysRevB.98.094301

    2018 doi

  51. [59]

    D. J. Evans, E. G. D. Cohen and G. P . Morriss,Probability of 2nd law violations in shearing steady-states, Phys. Rev. Lett. 71(15), 2401 (1993)

    1993

  52. [60]

    Gallavotti, Nonequilibrium and Irreversibility, Theoretical and Mathematical Physics

    G. Gallavotti, Nonequilibrium and Irreversibility, Theoretical and Mathematical Physics. Springer, doi:10.1007/978-3-319-06758-2 (2014)

    2014 doi

  53. [61]

    P . I. Hurtado, C. Pérez-Espigares, J. J. del Pozo and P . L. Garrido,Symmetries in fluctua- tions far from equilibrium, Proc. Natl. Acad. Sci. USA 108(19), 7704 (2011)

    2011

  54. [62]

    Villavicencio-Sanchez, R

    R. Villavicencio-Sanchez, R. J. Harris and H. Touchette, Fluctuation relations for anisotropic systems, Europhys. Lett. 105(3), 30009 (2014)

    2014

  55. [63]

    Lacoste and P

    D. Lacoste and P . Gaspard, Isometric fluctuation relations for equilibrium states with broken symmetry, Phys. Rev. Lett. 113(24), 240602 (2014). 66 SciPost Physics Lecture Notes Submission

    2014

  56. [64]

    Gaspard, Multivariate fluctuation relations for currents , New J

    P . Gaspard, Multivariate fluctuation relations for currents , New J. Phys. 15, 115014 (2013)

    2013

  57. [65]

    Pérez-Espigares, F

    C. Pérez-Espigares, F . Redig and C. Giardinà, Spatial fluctuation theorem , J. Phys. A 48(35), 35FT01 (2015)

    2015

  58. [66]

    Zarfaty and B

    L. Zarfaty and B. Meerson, Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry, J. Stat. Mech. P033304 (2016)

    2016

  59. [67]

    Vaikuntanathan, T

    S. Vaikuntanathan, T . R. Gingrich and P . L. Geissler,Dynamic phase transitions in simple driven kinetic networks, Phys. Rev. E 89(6), 062108 (2014)

    2014

  60. [68]

    K. D. N. T . Lam, J. Kurchan and D. Levine,Order in extremal trajectories, J. Stat. Phys. 137(5-6), 1079 (2009)

    2009

  61. [69]

    Chandler and J

    D. Chandler and J. P . Garrahan,Dynamics on the way to forming glass: bubbles in space- time., Annu. Rev. Phys. Chem. 61, 191 (2010)

    2010

  62. [70]

    Shpielberg and E

    O. Shpielberg and E. Akkermans, Le Chatelier principle for out-of-equilibrium and boundary-driven systems: Application to dynamical phase transitions , Phys. Rev. Lett. 116(24), 240603 (2016)

    2016

  63. [71]

    Y. Baek, Y. Kafri and V . Lecomte,Dynamical phase transitions in the current distribution of driven diffusive channels, J. Phys. A 51(10), 105001 (2018)

    2018

  64. [72]

    Yang and T .-D

    C.-N. Yang and T .-D. Lee,Statistical theory of equations of state and phase transitions. i. Theory of condensation, Phys. Rev. 87(3), 404 (1952)

    1952

  65. [73]

    Arndt,Yang-Lee theory for a nonequilibrium phase transition, Phys

    P . Arndt,Yang-Lee theory for a nonequilibrium phase transition, Phys. Rev. Lett. 84, 814 (2000)

    2000

  66. [74]

    R. A. Blythe and M. R. Evans, Lee-Yang zeros and phase transitions in nonequilibrium steady states, Phys. Rev. Lett. 89(8), 080601 (2002)

    2002

  67. [75]

    Dammer, S

    S. Dammer, S. Dahmen and H. Hinrichsen, Yang-Lee zeros for a nonequilibrium phase transition, J. Phys. A 35(21), 4527 (2002)

    2002

  68. [76]

    Blythe and M

    R. Blythe and M. Evans, The Lee-Yang theory of equilibrium and nonequilibrium phase transitions, Braz. J. Phys. 33, 464 (2003)

    2003

  69. [77]

    Flindt and J

    C. Flindt and J. Garrahan, Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics, Phys. Rev. Lett. 110(5), 050601 (2013)

    2013

  70. [78]

    Hickey , C

    J. Hickey , C. Flindt and J. Garrahan,Intermittency and dynamical Lee-Yang zeros of open quantum systems, Phys. Rev. E 90(6) (2014)

    2014

  71. [79]

    Brandner, V

    K. Brandner, V . Maisi, J. Pekola, J. Garrahan and C. Flindt,Experimental determination of dynamical Lee-Yang zeros, Phys. Rev. Lett. 118(18), 180601 (2017)

    2017

  72. [80]

    J. P . Garrahan, R. L. Jack, V . Lecomte, E. Pitard, K. van Duijvendijk and F . van Wijland, Dynamical first-order phase transition in kinetically constrained models of glasses , Phys. Rev. Lett.98(19), 195702 (2007)

    2007

  73. [81]

    J. P . Garrahan, R. L. Jack, V . Lecomte, E. Pitard, K. van Duijvendijk and F . van Wijland, First-order dynamical phase transition in models of glasses: an approach based on ensem- bles of histories, J. Phys. A 42(7), 075007 (2009). 67 SciPost Physics Lecture Notes Submission

    2009

  74. [82]

    L. O. Hedges, R. L. Jack, J. P . Garrahan and D. Chandler, Dynamic order-disorder in atomistic models of structural glass formers, Science 323(5919), 1309 (2009)

    2009

  75. [83]

    Pitard, V

    E. Pitard, V . Lecomte and F . Van Wijland,Dynamic transition in an atomic glass former: A molecular-dynamics evidence, Europhys. Lett. 96(5), 56002 (2011)

    2011

  76. [84]

    Speck, A

    T . Speck, A. Malins and C. P . Royall,First-order phase transition in a model glass former: Coupling of local structure and dynamics, Phys. Rev. Lett. 109(19), 195703 (2012)

    2012

  77. [85]

    Pinchaipat, M

    R. Pinchaipat, M. Campo, F . Turci, J. Hallett, T . Speck and C. P . Royall,Experimental evidence for a structural-dynamical transition in trajectory space , Phys. Rev. Lett. 119, 028004 (2017)

    2017

  78. [86]

    B. Abou, R. Colin, V . Lecomte, E. Pitard and F . van Wijland,Activity statistics in a colloidal glass former: experimental evidence for a dynamical transition , J. Chem. Phys. 148, 164502 (2018)

    2018

  79. [87]

    J. P . Garrahan, A. D. Armour and I. Lesanovsky ,Quantum trajectory phase transitions in the micromaser, Phys. Rev. E 84(2), 021115 (2011)

    2011

  80. [88]

    Genway , J

    S. Genway , J. P . Garrahan, I. Lesanovsky and A. D. Armour,Phase transitions in trajec- tories of a superconducting single-electron transistor coupled to a resonator, Phys. Rev. E 85(5), 051122 (2012)

    2012

  81. [89]

    Manzano and P

    D. Manzano and P . I. Hurtado, Symmetry and the thermodynamics of currents in open quantum systems, Phys. Rev. B 90(12), 125138 (2014)

    2014

  82. [90]

    Manzano and P

    D. Manzano and P . Hurtado, Harnessing symmetry to control quantum transport , Ad- vances in Physics 67, 1 (2018)

    2018

  83. [91]

    Manzano, M

    D. Manzano, M. Martínez-García and P . Hurtado, Coupled activity-current fluctuations in open quantum systems under strong symmetries, New J. Phys. 23(7), 073044 (2021), doi:https://doi.org/10.1088/1367-2630/ac0f19

    2021 doi

  84. [92]

    J. L. Doob, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. Fr. 85, 431 (1957)

    1957

  85. [93]

    R. L. Jack and P . Sollich, Large deviations and ensembles of trajectories in stochastic models, Prog. Theor. Phys. Supp. 184, 304 (2010), doi:10.1143 /PTPS.184.304

    2010

  86. [94]

    Chetrite and H

    R. Chetrite and H. Touchette, Variational and optimal control representations of condi- tioned and driven processes, J. Stat. Mech. P12001 (2015)

    2015

  87. [95]

    Chetrite and H

    R. Chetrite and H. Touchette, Nonequilibrium Markov processes conditioned on large deviations, Ann. Henri Poincare 16, 2005 (2015)

    2015

  88. [96]

    Carollo, J

    F . Carollo, J. P . Garrahan, I. Lesanovsky and C. Pérez-Espigares, Making rare events typical in Markovian open quantum systems , Phys. Rev. A 98, 010103 (2018), doi:10.1103/PhysRevA.98.010103

    2018 doi

  89. [97]

    Wilczek, Quantum time crystals , Phys

    F . Wilczek, Quantum time crystals , Phys. Rev. Lett. 109(16), 160401 (2012), doi:10.1103/PhysRevLett.109.160401

    2012 doi

  90. [98]

    Zakrzewski, Crystals of time, Physics 5, 116 (2012)

    J. Zakrzewski, Crystals of time, Physics 5, 116 (2012)

    2012

  91. [99]

    Sacha and J

    K. Sacha and J. Zakrzewski, Time crystals: a review , Rep. Prog. Phys. 81(1), 016401 (2018), doi:10.1088 /1361-6633/aa8b38. 68 SciPost Physics Lecture Notes Submission

    2018

  92. [100]

    Sacha, Time crystals, vol

    K. Sacha, Time crystals, vol. 114 of Springer Series on Atomic, Optical, and Plasma Physics, Springer (2020)

    2020

  93. [101]

    Hurtado-Gutiérrez, F

    R. Hurtado-Gutiérrez, F . Carollo, C. Pérez-Espigares and P . I. Hurtado, Building continuous time crystals from rare events , Phys. Rev. Lett. 125, 160601 (2020), doi:10.1103/PhysRevLett.125.160601

    2020 doi

  94. [102]

    Hurtado-Gutiérrez, P

    R. Hurtado-Gutiérrez, P . I. Hurtado and C. Pérez-Espigares, Spectral signatures of symmetry-breaking dynamical phase transitions, Phys. Rev. E 108, 014107 (2023)

    2023

  95. [103]

    Hurtado-Gutiérrez, C

    R. Hurtado-Gutiérrez, C. Pérez-Espigares and P . I. Hurtado,Programmable time crystals from higher-order packing fields, arXiv:2406.08581 (2024)

    2024 arXiv

  96. [104]

    Lecomte and J

    V . Lecomte and J. Tailleur,A numerical approach to large deviations in continuous time, J. Stat. Mech. P03004 (2007)

    2007

  97. [105]

    Giardinà, J

    C. Giardinà, J. Kurchan, V . Lecomte and J. Tailleur,Simulating rare events in dynamical processes, J. Stat. Phys. 145(4), 787 (2011)

    2011

  98. [106]

    G. M. Schutz, Exactly solvable models for many-body systems far from equilibrium , Phase Transitions Critical Phenomena, Vol 19 pp. 1–251 (2001), doi:10.1016 /S1062- 7901(01)80015-X

    2001

  99. [107]

    Lecomte, C

    V . Lecomte, C. Appert-Rolland and F . van Wijland,Thermodynamic formalism for systems with Markov dynamics , J. Stat. Phys. 127(1), 51 (2007), doi:10.1007 /s10955-006- 9254-0

    2007

  100. [108]

    Pérez-Espigares and P

    C. Pérez-Espigares and P . I. Hurtado,Sampling rare events across dynamical phase tran- sitions, Chaos 29, 083106 (2019), doi:10.1063 /1.5091669

    2019

  101. [109]

    Pérez-Espigares, F

    C. Pérez-Espigares, F . Carollo, J. P . Garrahan and P . I. Hurtado,Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation , Phys. Rev. E98, 060102 (2018), doi:10.1103 /PhysRevE.98.060102

    2018

  102. [110]

    Bodineau and B

    T . Bodineau and B. Derrida,Current large deviations for asymmetric exclusion processes with open boundaries, J. Stat. Phys. 123(2), 277 (2006)

    2006

  103. [111]

    Prados, A

    A. Prados, A. Lasanta and P . I. Hurtado,Nonlinear driven diffusive systems with dissipa- tion: Fluctuating hydrodynamics, Phys. Rev. E 86(3), 031134 (2012)

    2012

  104. [112]

    P . I. Hurtado and P . L. Krapivsky ,Compact waves in microscopic nonlinear diffusion, Phys. Rev. E85(6), 060103 (2012)

    2012

  105. [113]

    Gutiérrez-Ariza and P

    C. Gutiérrez-Ariza and P . I. Hurtado,The kinetic exclusion process: a tale of two fields, J. Stat. Mech. 103203 (2019)

    2019

  106. [114]

    P . I. Hurtado and P . L. Garrido,Current fluctuations and statistics during a large deviation event in an exactly solvable transport model, J. Stat. Mech. P02032 (2009)

    2009

  107. [115]

    Prados, A

    A. Prados, A. Lasanta and P . I. Hurtado, Large fluctuations in driven dissipative media , Phys. Rev. Lett.107(14), 140601 (2011)

    2011

  108. [116]

    P . I. Hurtado, A. Lasanta and A. Prados,Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation, Phys. Rev. E 88(2), 022110 (2013)

    2013

  109. [117]

    Žnidariˇc, Large-deviation statistics of a diffusive quantum spin chain and the additivity principle, Phys

    M. Žnidariˇc, Large-deviation statistics of a diffusive quantum spin chain and the additivity principle, Phys. Rev. E 89(4) (2014), doi:10.1103 /PhysRevE.89.042140. 69 SciPost Physics Lecture Notes Submission

    2014

  110. [118]

    Agranov, S

    T . Agranov, S. Ro, Y. Kafri and V . Lecomte, Macroscopic fluctuation theory and current fluctuations in active lattice gases , SciPost Phys. 14, 045 (2023), doi:10.21468/SciPostPhys.14.3.045

    2023 doi

  111. [119]

    Kipnis, C

    C. Kipnis, C. Marchioro and E. Presutti, Heat-flow in an exactly solvable model, J. Stat. Phys. 27(1), 65 (1982)

    1982

  112. [120]

    Spitzer, Interaction of markov processes , Adv

    F . Spitzer, Interaction of markov processes , Adv. Math. 5(2), 246 (1970), doi:10.1016/0001-8708(70)90034-4

    1970 doi

  113. [121]

    Gärtner, Convergence towards Burger’s equation and propagation of chaos for weakly asymmetric exclusion processes, Stoch

    J. Gärtner, Convergence towards Burger’s equation and propagation of chaos for weakly asymmetric exclusion processes, Stoch. Proc. Appl. 27, 233 (1987)

    1987

  114. [122]

    De Masi, E

    A. De Masi, E. Presutti and E. Scacciatelli, The weakly asymmetric simple exclusion process, Ann. Inst. Henri Poincaré 25(1), 1 (1989)

    1989

  115. [123]

    P . C. Martin, E. D. Siggia and H. A. Rose,Statistical dynamics of classical systems, Phys. Rev. A8, 423 (1973), doi:10.1103 /PhysRevA.8.423

    1973

  116. [124]

    G. B. Arfken, H. J. Weber and F . E. Harris,Mathematical methods for physicists: a com- prehensive guide, Academic Press (2011)

    2011

  117. [125]

    Saito and A

    K. Saito and A. Dhar,Additivity principle in high-dimensional deterministic systems, Phys. Rev. Lett.107(25), 250601 (2011)

    2011

  118. [126]

    Hardy , J

    G. Hardy , J. Littlewood and G. Pólya, Inequalities, Cambridge Mathematical Library . Cambridge University Press, ISBN 9780521358804 (1952)

    1952

  119. [127]

    M. R. Evans and T . Hanney ,Nonequilibrium statistical mechanics of the zero-range process and related models, J. Phys. A 38(19), R195 (2005)

    2005

  120. [128]

    Levine, D

    E. Levine, D. Mukamel and G. M. Schutz, Zero-range process with open boundaries , J. Stat. Phys. 120(5-6), 759 (2005)

    2005

  121. [129]

    Bertini, A

    L. Bertini, A. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Nonequilibrium current fluctuations in stochastic lattice gases, J. Stat. Phys. 123(2), 237 (2006)

    2006

  122. [130]

    R. L. Jack, I. R. Thompson and P . Sollich,Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems, Phys. Rev. Lett. 114(6), 060601 (2015)

    2015

  123. [131]

    Baek and Y

    Y. Baek and Y. Kafri, Singularities in large deviation functions, J. Stat. Mech. 2015(8), P08026 (2015)

    2015

  124. [132]

    Pérez-Espigares, I

    C. Pérez-Espigares, I. Lesanovsky , J. P . Garrahan and R. Gutiérrez,Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases , Phys. Rev. A 98, 021804 (2018), doi:10.1103 /PhysRevA.98.021804

    2018

  125. [133]

    Dematteis, T

    G. Dematteis, T . Grafke, M. Onorato and E. Vanden-Eijnden, Experimental evidence of hydrodynamic instantons: The universal route to rogue waves , Phys. Rev. X 9, 041057 (2019), doi:10.1103 /PhysRevX.9.041057

    2019

  126. [134]

    Gutiérrez and C

    R. Gutiérrez and C. Pérez-Espigares,Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents, Phys. Rev. E104, 044134 (2021), doi:10.1103 /PhysRevE.104.044134. 70 SciPost Physics Lecture Notes Submission

    2021

  127. [135]

    Cagnetta, F

    F . Cagnetta, F . Corberi, G. Gonnella and A. Suma,Large fluctuations and dynamic phase transition in a system of self-propelled particles , Phys. Rev. Lett. 119, 158002 (2017), doi:10.1103/PhysRevLett.119.158002

    2017 doi

  128. [136]

    Whitelam, K

    S. Whitelam, K. Klymko and D. Mandal, Phase separation and large de- viations of lattice active matter , J. Chem. Phys. 148(15), 154902 (2018), doi:https://doi.org/10.1063/1.5023403

    2018 doi

  129. [137]

    Tociu, E

    L. Tociu, E. Fodor, T . Nemoto and S. Vaikuntanathan,How dissipation constrains fluctu- ations in nonequilibrium liquids: Diffusion, structure, and biased interactions, Phys. Rev. X 9, 041026 (2019), doi:10.1103 /PhysRevX.9.041026

    2019

  130. [138]

    Gradenigo and S

    G. Gradenigo and S. Majumdar, A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle, J. Stat. Mech. 053206 2019(5) (2019), doi:10.1088/1742-5468/ab11be

    2019 doi

  131. [139]

    Nemoto, E

    T . Nemoto, E. Fodor, M. E. Cates, R. L. Jack and J. Tailleur, Optimizing active work: Dynamical phase transitions, collective motion, and jamming , Phys. Rev. E 99, 022605 (2019), doi:10.1103 /PhysRevE.99.022605

    2019

  132. [140]

    Cagnetta and E

    F . Cagnetta and E. Mallmin,Efficiency of one-dimensional active transport conditioned on motility, Phys. Rev. E 101, 022130 (2020), doi:10.1103 /PhysRevE.101.022130

    2020

  133. [141]

    Chiarantoni, F

    P . Chiarantoni, F . Cagnetta, F . Corberi, G. Gonnella and A. Suma,Work fluctuations of self-propelled particles in the phase separated state , J. Phys. A 53(36), 36LT02 (2020), doi:https://doi.org/10.1088/1751-8121/ab8f3c

    2020 doi

  134. [142]

    Fodor, T

    E. Fodor, T . Nemoto and S. Vaikuntanathan, Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles, New J. Phys. 22(1), 013052 (2020), doi:10.1088 /1367-2630/ab6353

    2020

  135. [143]

    GrandPre, K

    T . GrandPre, K. Klymko, K. K. Mandadapu and D. T . Limmer,Entropy production fluc- tuations encode collective behavior in active matter , Phys. Rev. E 103, 012613 (2021), doi:10.1103/PhysRevE.103.012613

    2021 doi

  136. [144]

    Y.-E. Keta, E. Fodor, F . van Wijland, M. E. Cates and R. L. Jack, Collective mo- tion in large deviations of active particles , Phys. Rev. E 103, 022603 (2021), doi:10.1103/PhysRevE.103.022603

    2021 doi

  137. [145]

    J. Yan, H. Touchette and G. M. Rotskoff, Learning nonequilibrium control forces to characterize dynamical phase transitions , Phys. Rev. E 105, 024115 (2022), doi:10.1103/PhysRevE.105.024115

    2022 doi

  138. [146]

    Flindt, C

    C. Flindt, C. Fricke, F . Hohls, T . Novotn`y, K. Netoˇcn`y, T . Brandes and R. Haug,Universal oscillations in counting statistics, Proc. Natl. Acad. Sci. USA 106(25), 10116 (2009)

    2009

  139. [147]

    J. P . Garrahan and I. Lesanovsky ,Thermodynamics of quantum jump trajectories, Phys. Rev. Lett.104(16), 160601 (2010)

    2010

  140. [148]

    C. Ates, B. Olmos, J. P . Garrahan and I. Lesanovsky ,Dynamical phases and intermittency of the dissipative quantum Ising model, Phys. Rev. A 85(4), 043620 (2012)

    2012

  141. [149]

    Hickey , S

    J. Hickey , S. Genway , I. Lesanovsky and J. Garrahan, Thermodynamics of quadrature trajectories in open quantum systems, Phys. Rev. A 86(6), 063824 (2012). 71 SciPost Physics Lecture Notes Submission

    2012

  142. [150]

    Lesanovsky , M

    I. Lesanovsky , M. van Horssen, M. Guta and J. P . Garrahan,Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state, Phys. Rev. Lett. 110(15), 150401 (2013)

    2013

  143. [151]

    Maisi, D

    V . Maisi, D. Kambly , C. Flindt and J. Pekola,Full counting statistics of Andreev tunneling, Phys. Rev. Lett.112(3), 036801 (2014)

    2014

  144. [152]

    J. J. Binney , N. J. Dowrick, A. J. Fisher and M. Newman,The Theory of Critical Phenom- ena: An Introduction to the Renormalization Group , Oxford University Press, Inc., New York, NY, USA, ISBN 0198513933, 9780198513933 (1992)

    1992

  145. [153]

    Vroylandt and G

    H. Vroylandt and G. Verley ,Non-equivalence of dynamical ensembles and emergent non- ergodicity, Journal of Statistical Physics174(2), 404 (2019), doi:10.1007/s10955-018- 2186-7

    2019 doi

  146. [154]

    Shapere and F

    A. Shapere and F . Wilczek, Classical time crystals , Phys. Rev. Lett. 109(16), 160402 (2012), doi:10.1103 /PhysRevLett.109.160402

    2012

  147. [155]

    Richerme,How to create a time crystal, Physics 10, 5 (2017)

    P . Richerme,How to create a time crystal, Physics 10, 5 (2017)

    2017

  148. [156]

    N. Y. Yao and C. Nayak,Time crystals in periodically driven systems, Physics Today71(9), 40 (2018), doi:10.1063 /pt.3.4020

    2018

  149. [157]

    Shpielberg, T

    O. Shpielberg, T . Nemoto and J. Caetano,Universality in dynamical phase transitions of diffusive systems, Phys. Rev. E 98, 052116 (2018)

    2018

  150. [158]

    Simon, Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries, J

    D. Simon, Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries, J. Stat. Mech. P07017 (07) (2009), doi:10.1088 /1742- 5468/2009/07/p07017

    2009

  151. [159]

    Popkov, G

    V . Popkov, G. M. Schütz and D. Simon,ASEP on a ring conditioned on enhanced flux, J. Stat. Mech. P10007 (10) (2010)

    2010

  152. [160]

    Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland Personal Library

    N. Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland Personal Library. Elsevier Science, ISBN 978-0-08-047536-3 (2011)

    2011

  153. [161]

    Tailleur and J

    J. Tailleur and J. Kurchan, Probing rare physical trajectories with Lyapunov weighted dynamics, Nature Phys. 3(3), 203 (2007)

    2007

  154. [162]

    Tailleur and V

    J. Tailleur and V . Lecomte,Simulation of large deviation functions using population dy- namics, Modeling Simulation New Materials 1091, 212 (2009)

    2009

  155. [163]

    Gaveau and L

    B. Gaveau and L. S. Schulman, Theory of nonequilibrium first-order phase transitions for stochastic dynamics, J. Math. Phys. 39(3), 1517 (1998), doi:10.1063 /1.532394

    1998

  156. [164]

    Hänggi and H

    P . Hänggi and H. Thomas, Stochastic processes: Time evolution, symmetries and lin- ear response , Phys. Rep. 88(4), 207 (1982), doi:https: //doi.org/10.1016/0370- 1573(82)90045-X

    1982 doi

  157. [165]

    Ledermann, On the asymptotic probability distribution for certain Markoff processes , Math

    W . Ledermann, On the asymptotic probability distribution for certain Markoff processes , Math. Proc. Cambr. Phil. Soc. 46(4), 581 (1950), doi:https://doi.org/10.1017/S0305004100026141

    1950 doi

  158. [166]

    Gaveau and L

    B. Gaveau and L. S. Schulman, Multiple phases in stochastic dynamics: Geometry and probabilities, Phys. Rev. E 73, 036124 (2006), doi:10.1103 /PhysRevE.73.036124. 72 SciPost Physics Lecture Notes Submission

    2006

  159. [167]

    Minganti, A

    F . Minganti, A. Biella, N. Bartolo and C. Ciuti,Spectral theory of liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018), doi:10.1103/PhysRevA.98.042118

    2018 doi

  160. [168]

    Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Phys

    B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Phys. Rep. 301(1-3), 65 (1998)

    1998

  161. [169]

    R. B. Potts, Some generalized order-disorder transformations, In Mathematical proceed- ings of the cambridge philosophical society, vol. 48, p. 106. Cambridge University Press (1952)

    1952

  162. [170]

    Moessner and S

    R. Moessner and S. L. Sondhi,Equilibration and order in quantum Floquet matter, Nature Physics 13(5), 424 (2017), doi:10.1038 /nphys4106

    2017

  163. [171]

    Kaviani and F

    S. Kaviani and F . H. Jafarpour, Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions , J. Stat. Mech. (1), 013210 (2020), doi:10.1088/1742-5468/ab5d0a

    2020 doi

  164. [172]

    Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer, New York (1984)

    Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer, New York (1984)

    1984

  165. [173]

    Kuramoto and I

    Y. Kuramoto and I. Nishikawa, Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities , J. Stat. Phys. 49(3), 569 (1987), doi:10.1007/BF01009349

    1987 doi

  166. [174]

    Daido, Order function and macroscopic mutual entrainment in uniformly coupled limit- cycle oscillators, Prog

    H. Daido, Order function and macroscopic mutual entrainment in uniformly coupled limit- cycle oscillators, Prog. Theor. Phys. 88(6), 1213 (1992), doi:10.1143 /ptp/88.6.1213

    1992

  167. [175]

    Pikovsky , M

    A. Pikovsky , M. Rosenblum and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge (2003)

    2003

  168. [176]

    J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F . Ritort and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena , Rev. Mod. Phys. 77(1), 137 (2005), doi:10.1103 /RevModPhys.77.137

    2005

  169. [177]

    Watanabe and M

    H. Watanabe and M. Oshikawa, Absence of quantum time crystals , Phys. Rev. Lett. 114(25), 251603 (2015), doi:10.1103 /PhysRevLett.114.251603

    2015

  170. [178]

    Spohn, Large Scale Dynamics of Interacting Particles, Theoretical and Mathematical Physics

    H. Spohn, Large Scale Dynamics of Interacting Particles, Theoretical and Mathematical Physics. Springer Berlin Heidelberg, ISBN 9783642843716 (2012)

    2012

  171. [179]

    Cereceda-López, A

    E. Cereceda-López, A. P . Antonov, A. Ryabov, P . Maass and P . Tierno, Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape , Nature Comm. 14(1), 6448 (2023), doi:10.1038 /s41467-023-41989-x

    2023

  172. [180]

    Cereceda-López, Non-Equilibrium Dynamics of Driven and Confined Colloidal Systems, Ph.D

    E. Cereceda-López, Non-Equilibrium Dynamics of Driven and Confined Colloidal Systems, Ph.D. thesis, Universidad de Barcelona (2023)

    2023

  173. [181]

    Cereceda-López, M

    E. Cereceda-López, M. Ostinato, A. Ortiz-Ambriz, A. V . Straube, M. Palassini and P . Tierno, Excluded volume induces buckling in optically driven colloidal rings , Phys. Rev. Res.6, L012044 (2024), doi:10.1103 /PhysRevResearch.6.L012044

    2024

  174. [182]

    C. Lutz, M. Kollmann and C. Bechinger,Single-file diffusion of colloids in one-dimensional channels, Phys. Rev. Lett.93(2), 026001 (2004), doi:10.1103/PhysRevLett.93.026001

    2004 doi

  175. [183]

    Villada-Balbuena, A

    A. Villada-Balbuena, A. Ortiz-Ambriz, P . Castro-Villarreal, P . Tierno, R. Castañeda Priego and J. M. Méndez-Alcaraz, Single-file dynamics of colloids in circular channels: Time scales, scaling laws and their universality , Phys. Rev. Res. 3, 033246 (2021), doi:10.1103/PhysRe...

    2021 doi

  176. [184]

    Lindblad, Generators of quantum dynamical semigroups , Comm

    G. Lindblad, Generators of quantum dynamical semigroups , Comm. In Math. Phys. 48(2), 119 (1976)

    1976

  177. [185]

    Breuer and F

    H. Breuer and F . Petruccione, The theory of open quantum systems , Oxford University Press (2002)

    2002

  178. [186]

    Tejero, D

    A. Tejero, D. Manzano and P . I. Hurtado, Atom-doped photon engine: Extracting me- chanical work from a quantum system via radiation pressure, Phys. Rev. E 109, 024141 (2024), doi:10.1103 /PhysRevE.109.024141

    2024

  179. [187]

    Tejero, D

    A. Tejero, D. Manzano and P . I. Hurtado, Squeezing light to get non-classical work in quantum engines, arxiv:2408.15085 (2024), doi:10.48550 /arXiv.2408.15085. 74

    2024 doi

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