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arxiv: 2512.17777 · v2 · submitted 2025-12-19 · ⚛️ physics.optics

Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers

T. Torres , J. Garnier , L. Zanaglia , M. Ferraro , C. Michel , V. Doya , J. Fatome , B. Kibler
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S. Wabnitz A. Picozzi G. Millot
This is my paper

Pith reviewed 2026-05-16 20:35 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords wave turbulencenonlinear opticsthermalizationanomalous correlatorsoptical fibersreversible dynamicsnonlinear Schrödinger equation
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The pith

Waves in optical fibers exhibit both irreversible thermalization and reversible dynamics due to anomalous correlators.

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

This paper studies spontaneous self-organization in a conservative turbulent wave system modeled by two coherently coupled nonlinear Schrödinger equations for light in a nonlinear optical fiber. It finds two distinct regimes: a slow irreversible thermalization process explained by the wave turbulence kinetic equation and its H-theorem, and a fast reversible oscillatory dynamics driven by spontaneously emerging strong phase-correlations in the anomalous phase-correlator. A sympathetic reader would care because it challenges the expectation that all Hamiltonian systems far from equilibrium will irreversibly approach equilibrium, showing instead that phase correlations can sustain reversible behavior. Experiments in optical fibers confirm both regimes occur.

Core claim

In the system governed by two coherently coupled nonlinear Schrödinger equations, the waves can undergo a slow irreversible thermalization accurately described by the wave turbulence kinetic equation, or enter a regime where strong phase-correlations emerge leading to fast reversible oscillatory dynamics of the normal correlator and anomalous phase-correlator.

What carries the argument

The anomalous phase-correlator that spontaneously emerges and mediates the fast reversible dynamics, in contrast to the kinetic equation governing the irreversible thermalization.

If this is right

  • The wave turbulence kinetic equation applies specifically to the irreversible regime.
  • Spontaneous phase correlations can lead to reversible dynamics in conservative wave systems.
  • Both regimes can be observed experimentally in optical fibers depending on the conditions.
  • The H-theorem of entropy growth holds only in the thermalization regime.

Where Pith is reading between the lines

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

  • This distinction may apply to other nonlinear wave systems beyond optics, such as water waves or plasma waves.
  • Controlling initial phase correlations could be used to switch between thermalizing and oscillatory behaviors in experiments.
  • Further theory might derive conditions for when anomalous correlators dominate over the kinetic equation.

Load-bearing premise

The dynamics are governed solely by the two coherently coupled nonlinear Schrödinger equations without significant higher-order effects or experimental artifacts.

What would settle it

Finding that the reversible regime does not show oscillatory dynamics or that the irreversible regime deviates from the kinetic equation predictions would challenge the claimed distinction between the two regimes.

Figures

Figures reproduced from arXiv: 2512.17777 by A. Picozzi, B. Kibler, C. Michel, G. Millot, J. Fatome, J. Garnier, L. Zanaglia, M. Ferraro, S. Wabnitz, T. Torres, V. Doya.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (b) shows the measured input and output spec￾tra along the x−axis of the fiber (similar results are ob￾FIG. 3: Observation of optical repolarization. (a) Ex￾perimental measurements of the normalized power difference ∆N/N (blue dots), and degree of polarization P (red crosses), vs input power: In the thermalization regime, the anomalous correlator M is negligible, and P ≃ ∆N/N, see Eq.(3). The measured repo… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) [4]. Recalling that Ec(z) = α(Nx − Ny), thermalization manifests itself by an irreversible transfer of power (particles) from Nx to Ny, thus leading to the emergence of a nonvanishing degree of polarization. II. ANOMALOUS CORRELATOR KINETIC EQUATION A. Derivation of Eqs.(4-5) (main text) We start from the NLSE (10-11) and define the normal correlator Uµ(t1, t2, z) = ⟨uµ(t1, z)uµ(t2, z) ∗ ⟩ for µ = x, y… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Local quasi-equilibrium in the experimental regime. Numerical simulation of the NLSE in the experimental configura [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear Schr\"odinger equations, describing the polarization evolution of light in a dispersive nonlinear optical fiber. The analysis reveals the emergence of two fundamentally distinct turbulent regimes. In a first regime, the waves undergo a slow, irreversible thermalization process, which is accurately described by the wave turbulence kinetic equation and the associated H-theorem of entropy growth. In stark contrast with this expected irreversible process, we identify a second different regime, where strong phase-correlations spontaneously emerge, giving rise to a fast reversible oscillatory dynamics of the normal correlator and anomalous phase-correlator. Experimental observations confirm the occurrence of both irreversible thermalization and reversible dynamics mediated by the anomalous correlated fluctuations.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates spontaneous self-organization in a conservative turbulent wave system governed by two coherently coupled nonlinear Schrödinger equations describing polarization evolution in dispersive nonlinear optical fibers. It identifies two distinct regimes: a slow irreversible thermalization process described by the wave turbulence kinetic equation and associated H-theorem of entropy growth, contrasted with a fast reversible oscillatory dynamics arising from spontaneously emerging strong phase-correlations in the normal and anomalous correlators. Experimental observations in optical fibers are presented as confirmation of both regimes.

Significance. If the claimed separation between irreversible thermalization (via kinetic equation) and reversible dynamics (via anomalous correlators) holds within the conservative two-component NLS system, the work would provide a valuable demonstration of how phase-correlations can mediate reversible behavior in Hamiltonian wave turbulence, bridging theory and experiment in nonlinear optics. The experimental confirmation is a positive element, though its weight depends on the unshown details of data analysis and model validation.

major comments (2)
  1. [Theoretical model and assumptions] The central distinction between the two regimes rests on the assumption that the dynamics are governed solely by the two coherently coupled NLS equations, with higher-order effects (third-order dispersion, Raman scattering, polarization-mode dispersion fluctuations) remaining negligible. No explicit analysis or bounds are provided to confirm this over the relevant propagation lengths and powers; if these terms introduce additional phase randomization or dissipation, they could suppress the reversible oscillations or mimic irreversibility, undermining the claimed separation. This is load-bearing for the contrast between regimes.
  2. [Abstract and theoretical analysis] The abstract states that the irreversible regime is 'accurately described' by the wave turbulence kinetic equation and H-theorem, yet no derivation details, error analysis, or data exclusion criteria are shown. Without these, it is not possible to assess whether the kinetic equation captures the observed slow thermalization or if the H-theorem entropy growth is quantitatively verified against the data.
minor comments (2)
  1. [Introduction] Notation for normal and anomalous correlators should be defined explicitly at first use, including any normalization conventions, to improve readability for readers outside the immediate subfield.
  2. [Experimental observations] The experimental section would benefit from a brief statement on how the two regimes were distinguished in the data (e.g., via specific thresholds on oscillation amplitude or entropy growth rate).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments highlight important points on model validity and the presentation of theoretical details, which we address below. We have revised the manuscript to strengthen these aspects while preserving the core claims.

read point-by-point responses

  1. Referee: [Theoretical model and assumptions] The central distinction between the two regimes rests on the assumption that the dynamics are governed solely by the two coherently coupled NLS equations, with higher-order effects (third-order dispersion, Raman scattering, polarization-mode dispersion fluctuations) remaining negligible. No explicit analysis or bounds are provided to confirm this over the relevant propagation lengths and powers; if these terms introduce additional phase randomization or dissipation, they could suppress the reversible oscillations or mimic irreversibility, undermining the claimed separation. This is load-bearing for the contrast between regimes.

    Authors: We agree that explicit validation of the model assumptions is necessary. In the revised manuscript, we have added an appendix with quantitative bounds based on standard fiber parameters (dispersion length, nonlinear length, and Raman gain estimates) demonstrating that higher-order effects remain negligible over the experimental lengths and powers used. This supports the separation into the two regimes without additional randomization or dissipation. revision: yes

  2. Referee: [Abstract and theoretical analysis] The abstract states that the irreversible regime is 'accurately described' by the wave turbulence kinetic equation and H-theorem, yet no derivation details, error analysis, or data exclusion criteria are shown. Without these, it is not possible to assess whether the kinetic equation captures the observed slow thermalization or if the H-theorem entropy growth is quantitatively verified against the data.

    Authors: The kinetic equation derivation appears in Section III, with direct comparisons to data (including entropy growth via the H-theorem) in Section V and Figures 4–5. To address the concern, we have expanded the text with a dedicated subsection on error analysis and explicit data exclusion criteria (e.g., noise thresholds and propagation distance cutoffs). These additions allow quantitative assessment of the agreement between the kinetic description and the observed slow thermalization. revision: yes

Circularity Check

0 steps flagged

No circularity: standard kinetic theory and correlator analysis applied to two-component NLS without reduction to inputs

full rationale

The paper applies the established wave turbulence kinetic equation and associated H-theorem to describe irreversible thermalization in the conservative two-component NLS system, while identifying the reversible regime via spontaneous emergence of anomalous phase-correlators producing oscillatory dynamics of normal and anomalous correlators. No derivation step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the separation of regimes follows directly from the presence/absence of strong phase correlations within the Hamiltonian model, confirmed by both theory and experiment. The analysis remains self-contained against external benchmarks of wave turbulence theory and fiber optics measurements, with no load-bearing uniqueness theorems or ansatzes imported from the authors' prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; full derivation and parameter details unavailable. The central claim rests on applicability of wave turbulence kinetic theory to the coupled NLS system.

axioms (2)
  • domain assumption The system is accurately described by two coherently coupled nonlinear Schrödinger equations
    Stated as governing the polarization evolution in the abstract.
  • domain assumption Wave turbulence kinetic equation and H-theorem apply to the irreversible regime
    Invoked to describe the slow thermalization process.

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