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arxiv: 2605.18093 · v1 · pith:67MVLCDVnew · submitted 2026-05-18 · 🧮 math-ph · cond-mat.stat-mech· math.MP

Where solitons are in a KdV soliton gas

Benjamin Doyon This is my paper

Pith reviewed 2026-05-20 00:45 UTC · model grok-4.3

classification 🧮 math-ph cond-mat.stat-mechmath.MP
keywords KdV equationsoliton gasfluid-cell projectiondensity of statesBethe equationsintegrable hydrodynamicstau function
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The pith

Solitons in a KdV gas are located using a fluid-cell projection that preserves the field in mesoscopic regions.

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

The paper defines the positions of solitons in a dense KdV soliton gas by means of a fluid-cell projection. This projection ensures that removing solitons outside a mesoscopic region leaves the KdV field unchanged inside it, yielding a multi-soliton solution supported there. The weak limit of conserved densities is shown to be evaluable from the density of states. On large scales, the soliton positions satisfy the semi-classical Bethe equations that incorporate two-body scattering shifts. The proofs rely on a new tau function for the multi-soliton solution, which also yields bounds on the field's support and derivatives.

Core claim

We introduce soliton positions in the KdV multi-soliton field at finite density through a fluid-cell projection. Projecting out solitons outside a mesoscopic region leaves the field invariant in that region and produces a multi-soliton field supported exactly there. The weak limits of conserved densities equal integrals against the density of states. The positions obey the semi-classical Bethe equations on large scales, reproducing the kinetic equation of the soliton gas.

What carries the argument

A novel tau function for the multi-soliton KdV field that defines the fluid-cell projection of soliton positions

If this is right

  • The weak limit of conserved densities can be evaluated using the density of states.
  • On large scales the solitons' positions satisfy the semi-classical Bethe equations.
  • The kinetic equation of the KdV soliton gas is reproduced via a non-rigorous derivation.
  • New bounds are obtained on the growth of the multi-soliton support and on the supremum of the field and its derivatives.

Where Pith is reading between the lines

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

  • This definition may extend to other integrable soliton equations such as the nonlinear Schrödinger equation.
  • It provides a classical counterpart to position operators in generalised hydrodynamics for quantum systems.
  • Explicit computations with finite numbers of solitons could verify the projection properties directly.

Load-bearing premise

The novel tau function for the multi-soliton KdV field exists and satisfies the required properties under the stated conditions on spectral parameters and impact parameters.

What would settle it

An explicit calculation for a finite number of solitons with chosen impact parameters that checks whether the projected field exactly matches the restricted multi-soliton solution in the fluid cell would confirm or refute the projection property.

Figures

Figures reproduced from arXiv: 2605.18093 by Benjamin Doyon.

Figure 1
Figure 1. Figure 1: A representation of the time-of-flight thought experiment. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Magnifying glass effect: cartoon illustration of how magnifying-glass positions [PITH_FULL_IMAGE:figures/full_fig_p048_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the integration of the mollified signed density, [PITH_FULL_IMAGE:figures/full_fig_p064_3.png] view at source ↗
read the original abstract

The Korteweg-De Vries (KdV) equation is a paradigmatic model of integrable classical fields, admitting solitoning solutions. When many solitons are near to each other, their shapes are modified, and it is not manifest, from the KdV field, where they are. This is a key problem in the analysis of a soliton gas, as its main object, the density of states, is a number of solitons per unit length. How to define solitons' positions at finite densities in the macroscopic limit? A sensible criterium is that, projecting out solitons lying outside a mesoscopic region, the KdV field is unchanged in this region, and the result is a multi-soliton field supported there. In the context of emergent hydrodynamics, this is referred to as a fluid-cell projection. In this paper we solve this problem. We define solitons' positions and a fluid-cell projection, and show that it has these properties, without introducing radiative corrections. We show that the weak limit of conserved densities can be evaluated using the density of states. On large scales the solitons' positions satisfy the semi-classical Bethe equations introduced in the context Generalised Hydrodynamics, that accounts for the two-body scattering shift and encodes factorised scattering. A non-rigorous derivation reproduces the kinetic equation of the KdV soliton gas, first proposed by Gennady El in 2003 using Witham modulation theory from finite-gap solutions. The results hold under simple conditions on spectral parameters, and certain physically natural conditions on impact parameters. No randomness is required. Our proof is based on a novel tau function for the multi-soliton KdV field, which also allows us to obtain new bounds on the growth of the multi-soliton support and on the supremum of the field and its derivatives. We believe the methods are generalisable to other solitonic models.

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

3 major / 2 minor

Summary. The paper introduces a novel tau function for the multi-soliton KdV field to define solitons' positions at finite densities via a fluid-cell projection. It claims this projection leaves the KdV field unchanged inside a mesoscopic cell without radiative corrections, that weak limits of conserved densities are given by the density of states, and that large-scale soliton positions obey the semi-classical Bethe equations of generalised hydrodynamics. A non-rigorous derivation of the 2003 kinetic equation is recovered, all under stated conditions on spectral parameters and impact parameters; new bounds on support growth and field derivatives are also obtained.

Significance. If the claims hold, the work would supply a deterministic, non-random construction for soliton positions and hydrodynamics in the KdV soliton gas, directly addressing the definition of the density of states at finite density. The approach avoids radiative corrections and reproduces the expected kinetic equation, with potential generalisation to other integrable soliton models. The explicit tau-function bounds on support and derivatives constitute a concrete technical advance.

major comments (3)
  1. [Abstract] Abstract: the central assertion that the fluid-cell projection leaves the KdV field unchanged inside the cell without radiative corrections is load-bearing for all subsequent hydrodynamic claims, yet rests solely on the algebraic and analytic properties of the newly introduced tau function; no independent verification (e.g., explicit identity or limit) is indicated that these properties survive once impact parameters are chosen to produce finite density.
  2. [Derivation of weak limits] The section deriving the weak limits of conserved densities: the claim that these limits are evaluated using the density of states follows from the projection, but the argument supplies no check that the tau function satisfies the required KdV identities or that the projection commutes with the conserved quantities under the stated conditions on spectral parameters.
  3. [Large-scale Bethe equations] The large-scale analysis leading to the semi-classical Bethe equations: this step encodes the two-body scattering shift and factorised scattering, but it inherits the same dependence on the tau-function construction; if the projection fails to be exact for the chosen impact parameters, the connection to generalised hydrodynamics would not hold.
minor comments (2)
  1. [Abstract] The abstract refers to 'simple conditions on spectral parameters' and 'physically natural conditions on impact parameters' without listing them; an explicit statement early in the text would improve readability.
  2. [Introduction] Notation for the fluid-cell projection and the density of states could be introduced with a short table or diagram to clarify the mesoscopic scale relative to the soliton support.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major comment below, providing clarifications based on the existing proofs in the manuscript while indicating where additional details or verifications will be incorporated in the revision to address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central assertion that the fluid-cell projection leaves the KdV field unchanged inside the cell without radiative corrections is load-bearing for all subsequent hydrodynamic claims, yet rests solely on the algebraic and analytic properties of the newly introduced tau function; no independent verification (e.g., explicit identity or limit) is indicated that these properties survive once impact parameters are chosen to produce finite density.

    Authors: The manuscript establishes the fluid-cell projection through the explicit construction of the novel tau function, which satisfies the algebraic identities required to preserve the KdV field inside the mesoscopic cell. The conditions on impact parameters are chosen precisely to ensure finite density while maintaining these identities, as shown by direct evaluation of the tau function and the resulting field. To provide the suggested independent verification, we will add an explicit limiting case (e.g., a controlled expansion of the cell size) in the revised manuscript demonstrating that the field identity holds independently of the projection step itself. revision: partial

  2. Referee: [Derivation of weak limits] The section deriving the weak limits of conserved densities: the claim that these limits are evaluated using the density of states follows from the projection, but the argument supplies no check that the tau function satisfies the required KdV identities or that the projection commutes with the conserved quantities under the stated conditions on spectral parameters.

    Authors: The tau function is constructed to reproduce the standard multi-soliton solutions of the KdV equation, thereby satisfying the necessary identities by design. The weak limits are then obtained by integrating the conserved densities over the fluid cell after projection. We will revise the relevant section to include an explicit verification that the projection commutes with the conserved quantities under the given spectral parameter conditions, confirming the evaluation via the density of states. revision: yes

  3. Referee: [Large-scale Bethe equations] The large-scale analysis leading to the semi-classical Bethe equations: this step encodes the two-body scattering shift and factorised scattering, but it inherits the same dependence on the tau-function construction; if the projection fails to be exact for the chosen impact parameters, the connection to generalised hydrodynamics would not hold.

    Authors: The large-scale analysis follows directly from the positions defined by the exact fluid-cell projection, which we prove holds under the stated physically natural conditions on impact parameters. The two-body scattering shifts and factorised scattering then emerge from the asymptotic properties of the tau function. In the revision we will expand this part with a more detailed step-by-step derivation linking the projection to the semi-classical Bethe equations, reinforcing the connection to generalised hydrodynamics. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via novel tau function

full rationale

The paper constructs a novel tau function for the multi-soliton KdV field and uses it to define solitons' positions together with a fluid-cell projection. Under the stated conditions on spectral parameters and impact parameters, this construction is shown to preserve the KdV field inside the cell, to permit evaluation of weak limits of conserved densities from the density of states, and to imply that large-scale positions obey the semi-classical Bethe equations. Because the central results are obtained directly from the algebraic and analytic properties of the newly introduced tau function rather than from any fitted parameter, prior self-citation, or tautological redefinition of the target quantities, the derivation chain remains independent and self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

No free parameters are introduced; the work relies on standard mathematical assumptions for multi-soliton solutions and the existence of the novel tau function under the stated spectral and impact-parameter conditions.

axioms (2)
  • domain assumption KdV multi-soliton solutions exist and satisfy the stated conditions on spectral parameters and impact parameters.
    Invoked to guarantee the fluid-cell projection and hydrodynamic limits hold without radiative corrections.
  • standard math Standard properties of the KdV hierarchy and conserved densities.
    Background facts from integrable systems theory used to evaluate weak limits.

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Works this paper leans on

64 extracted references · 64 canonical work pages · 1 internal anchor

  1. [1]

    R. M. Miura, C. S. Gardner, and M. D. Kruskal. Korteweg-de vries equation and general- izations. ii. existence of conservation laws and constants of motion.Journal of Mathematical physics, 9(8):1204–1209, 1968

    work page 1968

  2. [2]

    C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura. Korteweg-devries equation and generalizations. vi. methods for exact solution.Communications on Pure and Applied Mathematics, 27(1):97–133, 1974

    work page 1974

  3. [3]

    V. E. Zakharov.What is integrability?Springer Science & Business Media, Berlin, Heidel- berg, 1991

    work page 1991

  4. [4]

    V. E. Zakharov. Kinetic equation for solitons.Sov. Phys. JETP, 33(3):538–540, 1971

    work page 1971

  5. [5]

    Thethermodynamiclimitofthewhithamequations.Physics Letters A,311(4):374– 383, 2003

    G.A.El. Thethermodynamiclimitofthewhithamequations.Physics Letters A,311(4):374– 383, 2003

    work page 2003

  6. [6]

    G. A. El and A. M. Kamchatnov. Kinetic equation for a dense soliton gas.Physical Review Letters, 95(20):204101, 2005

    work page 2005

  7. [7]

    G. A. El, A. M. Kamchatnov, M. V. Pavlov, and S. A. Zykov. Kinetic equation for a soliton gas and its hydrodynamic reductions.Journal of Nonlinear Science, 21:151–191, 2011

    work page 2011

  8. [8]

    M. V. Pavlov, V. B. Taranov, and G. A. El. Generalized hydrodynamic reductions of the kinetic equation for a soliton gas.Theoretical and Mathematical Physics, 171:675–682, 2012

    work page 2012

  9. [9]

    A. V. Gurevich, N. G. Mazur, and K. P. Zybin. Statistical limit in a completely inte- grable system with deterministic initial conditions.Journal of Experimental and Theoretical Physics, 90(4):695–713, 2000. 81

    work page 2000

  10. [10]

    O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura. Emergent hydrodynamics in integrable quantum systems out of equilibrium.Physical Review X, 6(4):041065, 2016

    work page 2016

  11. [11]

    Bertini, M

    B. Bertini, M. Collura, J. De Nardis, and M. Fagotti. Transport in out-of-equilibrium xxz chains: Exact profiles of charges and currents.Physical Review Letters, 117(20):207201, 2016

    work page 2016

  12. [12]

    G. A. El. Soliton gas in integrable dispersive hydrodynamics.Journal of Statistical Mechan- ics: Theory and Experiment, 2021(11):114001, 2021

    work page 2021

  13. [13]

    Suret, S

    P. Suret, S. Randoux, A. Gelash, D. Agafontsev, B. Doyon, and G. El. Soliton gas: Theory, numerics, and experiments.Physical Review E, 109(6):061001, 2024

    work page 2024

  14. [14]

    B. Doyon. Lecture notes on generalised hydrodynamics.SciPost Physics Lecture Notes, page 018, 2020

    work page 2020

  15. [15]

    Bastianello, B

    A. Bastianello, B. Bertini, B. Doyon, and R. Vasseur. Introduction to the special issue on emergenthydrodynamicsinintegrablemany-bodysystems.Journal of Statistical Mechanics: Theory and Experiment, 2022(1):014001, 2022

    work page 2022

  16. [16]

    Spohn.Hydrodynamic Scales of Integrable Many-Body Systems

    H. Spohn.Hydrodynamic Scales of Integrable Many-Body Systems. World Scientific, 2024

    work page 2024

  17. [17]

    Doyon, S

    B. Doyon, S. Gopalakrishnan, F. Møller, J. Schmiedmayer, and R. Vasseur. Generalized hydrodynamics: A perspective.Physical Review X, 15(1):010501, 2025

    work page 2025

  18. [18]

    Babelon, D

    O. Babelon, D. Bernard, and M. Talon.Introduction to classical integrable systems. Cam- bridge University Press, Cambridge, 2003

    work page 2003

  19. [19]

    Derezinski and C

    J. Derezinski and C. Gérard.Scattering theory of classical and quantum N-particle systems. Springer Science & Business Media, Berlin, Heidelberg, 2013

    work page 2013

  20. [20]

    Cambridge university press Cambridge, Cambridge, 1999

    M Takahashi.Thermodynamics of one-dimensional solvable models. Cambridge university press Cambridge, Cambridge, 1999

    work page 1999

  21. [21]

    The sine-gordon solitons as an n-body problem.Physics Letters B, 317(3):363–368, 1993

    Olivier Babelon and Denis Bernard. The sine-gordon solitons as an n-body problem.Physics Letters B, 317(3):363–368, 1993

    work page 1993

  22. [22]

    P. A. Ferrari, C. Nguyen, L. T. Rolla, and M. Wang. Soliton decomposition of the box-ball system. InForum of Mathematics, Sigma, volume 9, page e60. Cambridge University Press, 2021

    work page 2021

  23. [23]

    D. A. Croydon and M. Sasada. Generalized hydrodynamic limit for the box–ball system. Communications in Mathematical Physics, 383(1):427–463, 2021

    work page 2021

  24. [24]

    Aggarwal

    A. Aggarwal. Effective velocities in the toda lattice.Communications on Pure and Applied Mathematics, page e70046, 2025

    work page 2025

  25. [25]

    Aggarwal

    A. Aggarwal. Asymptotic scattering relation for the toda lattice, 2026. 82

    work page 2026

  26. [26]

    Generalized hydrodynamics in strongly interacting 1d bose gases.Science, 373(6559):1129– 1133, 2021

    Neel Malvania, Yicheng Zhang, Yuan Le, Jerome Dubail, Marcos Rigol, and David S Weiss. Generalized hydrodynamics in strongly interacting 1d bose gases.Science, 373(6559):1129– 1133, 2021

    work page 2021

  27. [27]

    J. Jendrej. Recent progress on the problem of soliton resolution.Eur. Math. Soc. Mag., 135:5–11, 2025

    work page 2025

  28. [28]

    Jenkins and A

    R. Jenkins and A. Tovbis. Approximation of the thermodynamic limit of finite-gap solutions to the focusing nls hierarchy by multisoliton solutions.Communications in Mathematical Physics, 406(9):214, 2025

    work page 2025

  29. [29]

    D. Sh. Lundina. Compactness of sets of reflection less potentials.Teor. Funktsii Funktsional. Anal. Prilozhen., 44:57–66, 1985

    work page 1985

  30. [30]

    Gesztesy, W

    E. Gesztesy, W. Karwowski, and Z Zhao. Limits of soliton solutions.Duke Mathematical Journal, 68(1):101–150, 1992

    work page 1992

  31. [31]

    Doyon, T

    B. Doyon, T. Yoshimura, and J.-S. Caux. Soliton gases and generalized hydrodynamics. Physical review letters, 120(4):045301, 2018

    work page 2018

  32. [32]

    B. Doyon. Generalized hydrodynamics of the classical toda system.Journal of Mathematical Physics, 60(7):073302, 2019

    work page 2019

  33. [33]

    Congy, G

    T. Congy, G. El, and G. Roberti. Soliton gas in bidirectional dispersive hydrodynamics. Physical Review E, 103(4):042201, 2021

    work page 2021

  34. [34]

    Bonnemain, B

    T. Bonnemain, B. Doyon, and G. El. Generalized hydrodynamics of the kdv soliton gas. Journal of Physics A: Mathematical and Theoretical, 55(37):374004, 2022

    work page 2022

  35. [35]

    Soliton gas of the integrable boussinesq equation and its generalised hydrodynamics.SciPost Physics, 18(2):075, 2025

    Thibault Bonnemain and Benjamin Doyon. Soliton gas of the integrable boussinesq equation and its generalised hydrodynamics.SciPost Physics, 18(2):075, 2025

    work page 2025

  36. [36]

    Doyon, F

    B. Doyon, F. Hübner, and T. Yoshimura. New classical integrable systems from generalized T ¯T-deformations.Physical Review Letters, 132(25):251602, 2024

    work page 2024

  37. [37]

    Spohn.Large scale dynamics of interacting particles

    H. Spohn.Large scale dynamics of interacting particles. Springer Science & Business Media, Berlin, Heidelberg, 1991

    work page 1991

  38. [38]

    Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets

    B. Doyon and F. Hübner. Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets.arXiv preprint arXiv:2307.09307, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  39. [39]

    Doyon, F

    B. Doyon, F. Hübner, and T. Yoshimura. GeneralisedT ¯T-deformations of classical free particles.Annales Henri Poincaré, 2026

    work page 2026

  40. [40]

    Bonnemain, V

    T. Bonnemain, V. Caudrelier, and B. Doyon. Hamiltonian formulation and aspects of integrability of generalised hydrodynamics.Annales Henri Poincaré, 27(1):287, 2025

    work page 2025

  41. [41]

    Urilyon, L

    A. Urilyon, L. Biagetti, J. Kethepalli, and J. De Nardis. Simulating generalised fluids via interacting wave packets evolution.Physical Review B, 113:014314, 2026. 83

    work page 2026

  42. [42]

    Kethepalli, A

    J. Kethepalli, A. Urilyon, T. Sadhu, and J. De Nardis. Ballistic macroscopic fluctuation theory via mapping to point particles.SciPost Physics, 20(4):105, 2026

    work page 2026

  43. [43]

    Urilyon, R

    A. Urilyon, R. Vasseur, S. Gopalakrishnan, and J. De Nardis. Anomalous diffusion and superdiffusion in integrable spin chains via a hard-rod gas mapping, 2026

    work page 2026

  44. [44]

    Takahashi and J

    D. Takahashi and J. Satsuma. A soliton cellular automaton.Journal of the Physical Society of Japan, 59(10):3514–3519, 1990

    work page 1990

  45. [45]

    Aggarwal and M

    A. Aggarwal and M. Nicoletti. Fluctuations for the toda lattice, 2026

    work page 2026

  46. [46]

    Bulchandani, X

    V. Bulchandani, X. Cao, and J. Moore. Kinetic theory of quantum and classical toda lattices.Journal of Physics A: Mathematical and Theoretical, 52:33LT01, 07 2019

    work page 2019

  47. [47]

    Fache, H

    L. Fache, H. Damart, F. Copie, T. Bonnemain, T. Congy, G. Roberti, P. Suret, G. El, and S. Randoux. Dissipation-driven emergence of a soliton condensate in a nonlinear electrical transmission line, 2024

    work page 2024

  48. [48]

    Bonnemain and S

    T. Bonnemain and S. Randoux. Exact charge, current, and velocity fields of interacting korteweg–de vries solitons.in preparation, 2026

    work page 2026

  49. [49]

    Kuijlaars and A

    A. Kuijlaars and A. Tovbis. On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems.Nonlinearity, 34(10):7227–7254, 2021

    work page 2021

  50. [50]

    M. J. Ablowitz and H. Segur.Solitons and the inverse scattering transform. SIAM, 1981

    work page 1981

  51. [51]

    Doyon and H

    B. Doyon and H. Spohn. Dynamics of hard rods with initial domain wall state.Journal of Statistical Mechanics: Theory and Experiment, 2017(7):073210, 2017

    work page 2017

  52. [52]

    Introduction to the hirota bilinear method

    Jarmo Hietarinta. Introduction to the hirota bilinear method. InIntegrability of Nonlinear Systems: Proceedings of the CIMPA School Pondicherry University, India, 8–26 January 1996, pages 95–103. Springer, 2007

    work page 1996

  53. [53]

    Cambridge university press, 1997

    Vladimir E Korepin, Vladimir E Korepin, NM Bogoliubov, and AG Izergin.Quantum inverse scattering method and correlation functions, volume 3. Cambridge university press, 1997

    work page 1997

  54. [54]

    A geometric viewpoint on gener- alized hydrodynamics.Nuclear Physics B, 926:570–583, 2018

    Benjamin Doyon, Herbert Spohn, and Takato Yoshimura. A geometric viewpoint on gener- alized hydrodynamics.Nuclear Physics B, 926:570–583, 2018

    work page 2018

  55. [55]

    B. Doyon. Exact large-scale correlations in integrable systems out of equilibrium.SciPost Physics, 5(5):054, 2018

    work page 2018

  56. [56]

    E. C. Titchmarsh.Introduction to Theory of Fourier Integrals. Oxford University Press, 1948

    work page 1948

  57. [57]

    Hübner, L

    F. Hübner, L. Biagetti, J. De Nardis, and B. Doyon. Diffusive hydrodynamics from long- range correlations.Physical Review Letters, 134:187101, 2025. 84

    work page 2025

  58. [58]

    Hydrodynamic noise in one dimension: projected kubo formula and how it vanishes in integrable models.SciPost Physics, 20(4):111, 2026

    Benjamin Doyon. Hydrodynamic noise in one dimension: projected kubo formula and how it vanishes in integrable models.SciPost Physics, 20(4):111, 2026

    work page 2026

  59. [59]

    Doyon and J

    B. Doyon and J. Myers. Fluctuations in ballistic transport from euler hydrodynamics. Annales Henri Poincaré, 21:255–302, 2020

    work page 2020

  60. [60]

    Myers, J

    J. Myers, J. M. Bhaseen, R. J. Harris, and B. Doyon. Transport fluctuations in integrable models out of equilibrium.SciPost Physics, 8(1):007, 2020

    work page 2020

  61. [61]

    Doyon, G

    B. Doyon, G. Perfetto, T. Sasamoto, and T. Yoshimura. Ballistic macroscopic fluctuation theory.SciPost Physics, 15(4):136, 2023

    work page 2023

  62. [62]

    Doyon, G

    B. Doyon, G. Perfetto, T. Sasamoto, and T. Yoshimura. Emergence of hydrodynamic spa- tial long-range correlations in nonequilibrium many-body systems.Physical review letters, 131(2):027101, 2023

    work page 2023

  63. [63]

    A. Kundu. Macroscopic fluctuation theory of correlations in hard rod gas.Journal of Statistical Mechanics: Theory and Experiment, 2025:103203, 2025

    work page 2025

  64. [64]

    Two-dimensionalstationary soliton gas.Physical Review Research, 7(1):013143, 2025

    T.Bonnemain, G.Biondini, B.Doyon, G.Roberti, andG.A.El. Two-dimensionalstationary soliton gas.Physical Review Research, 7(1):013143, 2025. 85

    work page 2025