arxiv: 2604.13104 · v1 · submitted 2026-04-10 · ❄️ cond-mat.stat-mech · hep-ph· hep-th

Recognition: unknown

Nonequilibrium crossover in the supercritical region from quench dynamics

Zi-Qiang Zhao , Zhang-Yu Nie , Jing-Fei Zhang , Xin Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:08 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech hep-phhep-th

keywords holographic superfluidsupercritical regionquench dynamicstopological defectsinvasion velocitynonequilibrium crossoverWidom linedynamical crossover

0 comments

The pith

Invasion velocity of topological defects turns at a specific point, defining a new nonequilibrium crossover line in the supercritical region.

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

The paper examines the post-quench evolution of a holographic superfluid model to probe subphases in the supercritical region from a dynamical viewpoint. Topological defects continue to invade the system even after the quench endpoint lies above the critical point, and the speed of this invasion varies with the final density ρ_f in a way that shows a distinct turning point. That turning point supplies a crossover line carrying both thermodynamic and kinetic content, supplying a nonequilibrium route to distinguish supercritical regimes that static response functions cannot access.

Core claim

In the holographic superfluid, a rapid quench across the critical point leaves the invasion phenomenon driven by topological defects intact in the supercritical region. The invasion velocity plotted against the quench endpoint density ρ_f displays a clear turning point; this turning point is identified as a new nonequilibrium supercritical crossover line. The line differs from the Widom line and the Frenkel line by incorporating kinetic information that reflects the dynamical character of the supercritical fluid under nonequilibrium drive.

What carries the argument

The turning point in invasion velocity versus quench endpoint ρ_f, which acts as the marker that locates the nonequilibrium crossover line.

If this is right

The supercritical region can be subdivided using dynamical signatures extracted from quench protocols rather than equilibrium thermodynamics alone.
Topological defects remain dynamically relevant above the critical point and their motion encodes crossover information.
The new line mixes thermodynamic data with kinetic data, giving a characterization unavailable from static correlation functions.
Nonequilibrium quench dynamics offers a general method for mapping subphases in systems where equilibrium approaches are limited to quasi-static regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same velocity-turning signature could be searched for in laboratory quenches of ultracold Bose gases or liquid helium to test whether the crossover appears outside holographic models.
If the turning point survives in other defect-bearing systems, it might supply a practical diagnostic for supercritical behavior in classical fluids or soft matter.
The approach suggests that kinetic observables measured after a quench can supplement or replace equilibrium lines such as the Widom line in strongly coupled systems.

Load-bearing premise

The turning point seen in the invasion velocity versus ρ_f truly locates a physically meaningful crossover rather than arising only from the numerical scheme or the holographic model itself.

What would settle it

Repeating the identical quench protocol in a non-holographic model such as the time-dependent Ginzburg-Landau or Gross-Pitaevskii equation and finding no turning point in invasion velocity as a function of final density would falsify the claim that the feature defines a general nonequilibrium crossover.

Figures

Figures reproduced from arXiv: 2604.13104 by Jing-Fei Zhang, Xin Zhang, Zhang-Yu Nie, Zi-Qiang Zhao.

**Figure 1.** Figure 1: FIG. 1. The condensate and free energy curve for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. The relationship between the invasion velocity in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

Distinguishing different subphases in the supercritical region is a fundamental issue in statistical physics and condensed matter physics. Traditional approaches mainly rely on static thermodynamic response functions or equilibrium correlation functions, which are inherently confined to quasi-static processes. In this work, we adopt a nonequilibrium dynamical perspective to investigate the evolution of a holographic superfluid model following a rapid quench across the critical point. We find that the invasion phenomenon induced by topological defects persists in the supercritical region, and the invasion velocity exhibits a clear turning point as a function of the quench endpoint $\rho_f$. This turning point defines a new nonequilibrium supercritical crossover line. In contrast to the classical Widom line or Frenkel line, this new crossover line encodes both thermodynamic information and kinetic information, reflecting the dynamical nature of the supercritical region under nonequilibrium conditions. This study provides a novel nonequilibrium dynamical approach for characterizing supercritical subphases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines a new supercritical crossover line in a holographic superfluid from the turning point in post-quench invasion velocity, but the claim needs checks against protocol changes to hold up.

read the letter

The main thing here is a dynamical characterization of supercritical subphases: after a rapid quench in the holographic model, the invasion of the condensate front from topological defects continues above criticality, and its velocity versus final density shows a turning point that the authors treat as a new crossover line mixing thermodynamic and kinetic information. This is distinct from the usual Widom or Frenkel lines, which are static. The holographic setup lets them evolve the bulk equations numerically and track the front directly, which is a reasonable way to bring in nonequilibrium dynamics. The abstract frames the contrast with equilibrium methods clearly and presents the turning point as an observed feature rather than something fitted in advance. That part is straightforward and new enough to note. The soft spots are in the support for calling the turning point a robust crossover. The description gives no quantitative method for locating it, no error estimates, and no tests of whether the location stays put when quench duration or initial defect density changes. If the feature moves under those variations, as the stress-test concern flags, it would be tied to this specific protocol rather than a general nonequilibrium property. The model itself is the standard Einstein-scalar holographic superfluid, so any claim to broader relevance for real fluids would need extra justification. No obvious circularity or invented entities show up. This is for people already working with holographic condensed-matter models or nonequilibrium fluid dynamics who want to explore dynamical subphase distinctions. A reader in statistical mechanics might pick up the idea if the numerics are solid, but would want the robustness data first. It deserves peer review because the core simulation is doable to verify and the angle is fresh, even if revisions on methods and checks are likely needed.

Referee Report

3 major / 2 minor

Summary. The manuscript studies the nonequilibrium quench dynamics of a holographic superfluid model across the critical point. It reports that the invasion of the condensate front induced by topological defects continues into the supercritical regime, and that the invasion velocity v(ρ_f) as a function of the final density exhibits a turning point; this feature is interpreted as defining a new nonequilibrium crossover line in the supercritical region that encodes both thermodynamic and kinetic information, distinct from the Widom or Frenkel lines.

Significance. If the turning point is shown to be robust and physically meaningful, the work would provide a concrete dynamical protocol for distinguishing supercritical subphases, extending beyond equilibrium response functions. The holographic approach supplies non-perturbative access to strongly coupled dynamics, which is a strength when the numerical evidence is placed on a firmer footing.

major comments (3)

[§4] §4 (Results on invasion velocity): The location of the turning point in v(ρ_f) is stated to be 'clear' but the quantitative criterion used to identify it (e.g., extremum of a derivative, change-point algorithm, or fitting procedure) is not specified, nor are statistical uncertainties or sensitivity to binning/resolution reported. This directly affects the central claim that the feature defines a crossover line.
[§3] §3 (Model and quench protocol): No systematic checks are presented on the dependence of the turning-point location on quench duration (e.g., varying the ramp time by a factor of two) or on initial defect density. Without these, it remains possible that the observed feature is an artifact of the specific holographic quench protocol rather than a fixed nonequilibrium crossover.
[§5] §5 (Discussion and interpretation): The assertion that the new line 'encodes both thermodynamic information and kinetic information' is not supported by any direct comparison between the turning-point locus and equilibrium thermodynamic quantities (specific heat, compressibility, or correlation lengths) computed in the same model; the connection remains qualitative.

minor comments (2)

[Introduction] The term 'invasion phenomenon' is used in the abstract and introduction without a concise definition or reference to its prior usage in the holographic-superfluid literature; a short clarifying sentence would improve readability.
[Figure captions] Figure captions for the velocity plots should explicitly state the numerical resolution, time-stepping scheme, and any convergence tests performed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped us identify areas for improvement in clarity and robustness. We address each major comment below and have prepared revisions to the manuscript accordingly.

read point-by-point responses

Referee: [§4] §4 (Results on invasion velocity): The location of the turning point in v(ρ_f) is stated to be 'clear' but the quantitative criterion used to identify it (e.g., extremum of a derivative, change-point algorithm, or fitting procedure) is not specified, nor are statistical uncertainties or sensitivity to binning/resolution reported. This directly affects the central claim that the feature defines a crossover line.

Authors: We agree that an explicit quantitative procedure is necessary. In the revised manuscript we will state that the turning point is identified as the density ρ_f at which the first derivative dv/dρ_f (computed via central finite differences with smoothing over three neighboring points) reaches its most negative value, corresponding to the inflection. Error bars are obtained from the standard deviation across an ensemble of 20 independent runs with different random initial defect configurations. We will also add a brief discussion of sensitivity to binning by showing that the identified location varies by less than 4% when the density bin width is changed by a factor of two. revision: yes
Referee: [§3] §3 (Model and quench protocol): No systematic checks are presented on the dependence of the turning-point location on quench duration (e.g., varying the ramp time by a factor of two) or on initial defect density. Without these, it remains possible that the observed feature is an artifact of the specific holographic quench protocol rather than a fixed nonequilibrium crossover.

Authors: We have now performed the requested checks. Additional simulations were carried out with ramp times halved and doubled relative to the original protocol, and with initial defect densities reduced and increased by a factor of two. In all cases the location of the turning point shifts by at most 6%, remaining within the statistical uncertainty of the original data set. These results will be presented in a new supplementary figure together with a short paragraph in §3 of the revised manuscript, demonstrating that the crossover feature is robust against reasonable variations in the quench protocol. revision: yes
Referee: [§5] §5 (Discussion and interpretation): The assertion that the new line 'encodes both thermodynamic information and kinetic information' is not supported by any direct comparison between the turning-point locus and equilibrium thermodynamic quantities (specific heat, compressibility, or correlation lengths) computed in the same model; the connection remains qualitative.

Authors: We accept that the original discussion was qualitative. In the revised manuscript we will add a direct comparison: we compute the specific heat and isothermal compressibility in the equilibrium holographic superfluid as functions of density in the supercritical regime and locate their maxima. The turning-point locus lies between the Widom line (specific-heat maximum) and the region of slowest relaxation times extracted from the same model. This quantitative overlay will be included in §5, supporting the claim that the new line incorporates both thermodynamic and kinetic information. revision: yes

Circularity Check

0 steps flagged

No circularity: observed turning point from quench dynamics defines the line

full rationale

The paper performs numerical quenches in the holographic superfluid model governed by the bulk Einstein-scalar equations, measures the invasion velocity of the condensate front after crossing the critical point, and reports that this velocity exhibits a turning point versus the quench endpoint ρ_f. The new nonequilibrium crossover line is then located at that observed turning point. This construction is not self-definitional, as the velocity data are generated from the independent dynamical evolution rather than fitted or presupposed to produce the turning point; no parameter is tuned to match a target feature, no self-citation supplies a uniqueness theorem that forces the result, and no ansatz is smuggled in. The approach remains self-contained against external benchmarks because the turning point is a direct output of the simulated nonequilibrium trajectories and can be checked by varying quench protocols or resolution without reference to the paper's own definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the holographic superfluid model captures the relevant physics and that the invasion velocity turning point meaningfully delineates subphases. No free parameters or invented entities are mentioned in the abstract.

axioms (1)

domain assumption Holographic duality accurately describes the dynamics of the superfluid model under quench
The entire study is performed within a holographic superfluid framework.

pith-pipeline@v0.9.0 · 5458 in / 1215 out tokens · 78925 ms · 2026-05-10T17:08:11.360303+00:00 · methodology

discussion (0)

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