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Ballistic macroscopic fluctuation theory via mapping to point particles

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Pith's one-line read This paper establishes that, for generic integrable models, the ballistic macroscopic fluctuation theory can be constructed by mapping interacting quasiparticles to free point particles with the scattering shift as an effective rod length.

desk verdict A technically solid reformulation of BMFT with a clearly flagged conjecture at its center: the initial-fluctuation functional is proven for hard rods, not for generic integrable models. read the letter →

arxiv 2505.18093 v1 pith:FLU5DIGX submitted 2025-05-23 cond-mat.stat-mech

Jitendra Kethepalli , Andrew Urilyon , Tridib Sadhu , Jacopo De Nardis This is my paper · ORCID
classification cond-mat.stat-mech PACS 05.60.-k05.40.-a05.70.Ln
keywords ballisticmacroscopicfluctuationtheorygeneralizedhydrodynamicsfullcountingstatisticsintegrablemodelspoint-particlemappingscatteringshiftlargedeviationshardrods
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

This paper claims that, for generic integrable models, the ballistic macroscopic fluctuation theory (BMFT) can be built by mapping the interacting quasiparticle gas onto non-interacting point particles, with the two-body scattering shift $a(\theta-\theta')$ playing the role of an effective rod length. In the free-particle coordinates, the initial density fluctuations are sampled from the free-particle large-deviation functional, and the subsequent evolution is just convection at bare velocity $\theta$. The authors derive from this the cumulant generating function $\mu(\lambda)$ for full counting statistics, Eq. (77), and the two-point normal-mode correlation, Eq. (123), and they show that the hard-rods limit reproduces the results of Refs. [24, 25] and Ref. [70]. If correct, this unifies the derivation of fluctuation statistics across integrable models and supports the picture that all late-time fluctuations come from initial noise propagated by Euler-scale hydrodynamics.

What carries the argument

The load-bearing object is the mapping of Eq. (4): interacting coordinates $x_i(t)$ are related to free coordinates $X_i(t)$ by a shift built from the two-body scattering shift $a(\theta_i-\theta_j)$, the direct generalization of the hard-rod length. This mapping converts a generic integrable model into a free-particle gas whose phase-space density $r_t(X,\theta)$ obeys the convective equation $\partial_t r_t + \theta\,\partial_X r_t = 0$, so that BMFT can be applied in its simplest free-particle form. The system-specific physics is then hidden entirely in the initial free-energy cost $\tilde{F}[r_0]$ of Eqs. (27)-(29), which distinguishes classical, Fermi-Dirac, and Bose-Einstein statistics.

What would settle it

Compute the full-counting-statistics cumulant $\kappa_3$ or the two-point correlation in a generic integrable model away from the hard-rod limit, such as the Lieb-Liniger gas, and compare with Eq. (77) or Eq. (123). A more direct test: sample initial GGE configurations, map them to free coordinates via Eq. (4), and measure the large-deviation functional of the mapped initial density; if it deviates from the free-particle form of Eq. (29), the general claim fails.

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Extended reading notes

Core claim

The central claim is that for generic integrable models, both the full counting statistics of transported charge and the two-point normal-mode correlation function can be obtained by first mapping the interacting quasiparticle coordinates $x_i$ to free-particle coordinates $X_i$ through the relation $x_i = X_i - \frac{1}{2}\sum_{j\neq i} a(\theta_i-\theta_j)\operatorname{sgn}(x_i-x_j)$, where $a(\theta_i-\theta_j)$ is the scattering shift acting as an effective rod length. In these free coordinates, the initial density fluctuations are governed by the free-particle large-deviation functional of Eqs. (27)-(29), and a saddle-point evaluation of the path integral directly yields the cumulant generating function $\mu(\lambda)$ in Eq. (77) and the correlation $C_{t_1,t_2}(x_1,\theta_1,x_2,\theta_2)$ in Eq. (123). The hard-rods limit reproduces the earlier BMFT results and the microscopic hard-rod correlation of Ref. [70], which the authors take as evidence that all late-time fluctuations and correlations derive from initial noise convected by Euler-scale hydrodynamics.

Load-bearing premise

The load-bearing assumption is that the initial fluctuations of the mapped point-particle density follow the free-particle large-deviation functional of Eqs. (27)-(29) for every integrable model; the paper proves this only for hard rods and states in Section 3 that a general proof is not available.

Editorial extensions

If this is right

  • The full counting statistics of charge transport in any integrable model are given by Eq. (77), and its first three cumulants in the partitioning protocol match the BMFT results of Refs. [24, 25].
  • The equal-time normal-mode correlation reduces in the hard-rods limit to Eq. (126), reproducing the microscopic derivation of Ref. [70].
  • All cumulants grow linearly in time $T$ because the saddle-point action scales linearly with $T$, which is the expected ballistic signature.
  • The derivation covers both classical and quantum statistics through the free-energy functional of Eq. (29), with Poissonian, Fermi-Dirac, and Bose-Einstein sampling.
  • The mapping corroborates that no bulk noise is needed: all statistics arise from initial fluctuations propagated by Euler-scale hydrodynamics.
  • The action is written directly in terms of quasiparticle phase-space densities rather than charge contents, making the BMFT action expressible with standard macroscopic-fluctuation-theory quantities.

Reading between the lines

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

  • If the free-particle form of the initial large-deviation functional holds beyond hard rods, the same action should yield diffusive corrections to the cumulants by expanding around the Euler solution; the authors mention such an extension as future work, but it is a direct corollary of their path-integral construction.
  • The rod-length interpretation suggests a testable deformation: adding an external potential or changing the particle statistics in the free-particle gas should produce corresponding BMFT predictions for integrable models with the same scattering shift, which could be checked numerically in, for example, the Lieb-Liniger gas.
  • A direct way to falsify the general claim would be to compute the true GGE fluctuation functional in the bare coordinates of a generic integrable model and compare it with the free-particle form of Eq. (29); any mismatch would alter the predicted cumulants outside the hard-rod limit.
  • The relation to the parallel hard-rods formulation of Ref. [72], noted by the authors, suggests that a direct comparison of the two phase-space formulations could simplify the derivation of correlation functions in hard-rod gases.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper proposes a ballistic macroscopic fluctuation theory (BMFT) construction for generic integrable models by mapping the interacting quasiparticle gas to noninteracting point particles, with the two-body scattering shift a(θ−θ′) playing the role of an effective rod length. Starting from a free-particle path integral and the free-particle large-deviation functional of Eqs. (27)–(29), the paper derives the full-counting-statistics cumulant generating function μ(λ) in Eq. (77) and the two-point normal-mode correlation in Eq. (123). The derivation is benchmarked against known hard-rod results and the partitioning protocol, and Fig. 4 reports a hard-rod numerical test of the rate function.

Significance. If the central conjecture holds, the paper provides a unified and methodologically clean derivation of ballistic fluctuation statistics in integrable models, and it corroborates the picture that late-time correlations are convected initial noise. The explicit benchmarks are genuine strengths: Eq. (95) reproduces the first three cumulants of Refs. [24,25] in the partitioning protocol, Eq. (126) matches Ref. [70] in the hard-rod limit, and the numerical test in Fig. 4 supports the non-Gaussian rate function for hard rods. However, the generality of the main claim is conditional on an unproven initial-fluctuation functional; the significance is therefore high but currently provisional.

major comments (2)
  1. [Section 3, Eq. (61); Appendix B.2] The central assumption is stated, not proven, at the point where it is first used: immediately after Eq. (61) the text says that the initial profile in point-particle coordinates is governed by the free-particle large-deviation functional of Eqs. (27)–(29), with the caveat 'While a general proof is not available.' The only proof, Appendix B.2, treats hard rods with constant rod length a, where the strip-width contraction ΔX = Δx − n_i a makes the mapped measure factorize as in Eqs. (156)–(158). For a generic integrable model the scattering shift a(θ−θ′) is rapidity dependent, so the mapping in Eq. (14) is nonlocal and the pushforward of the GGE measure is not shown to be the independent-particle measure of Eq. (29). Because Eqs. (73)–(77) and Eqs. (116)–(123) are all saddle-point consequences of this functional, Eqs. (77) and (123) are not supported for generic integrable models unless the assumption is established. I recommend either proving the large-deviation principle for a nontrivial class beyond hard rods or explicitly restricting the claims, including the title and abstract, to models for which the assumption can be justified.
  2. [Section 5 and Fig. 4] The central claim of the paper concerns generic integrable models, but every quantitative test and benchmark is in the hard-rod or partitioning-protocol setting. The analytic agreements quoted—Eq. (95) with Refs. [24,25] and Eq. (126) with Ref. [70]—are hard-rod or partitioning-protocol results, and the numerical test in Fig. 4 is for hard rods only. No test is provided for a model with rapidity-dependent scattering shift, such as Lieb-Liniger or another Bethe-ansatz model. Unless such a test is supplied, or the generic claim is explicitly downgraded to a conjecture, the manuscript overstates the degree to which the generic integrable case has been derived.
minor comments (6)
  1. [Eq. (64)] The displayed expression for Q_1 contains an extraneous λ multiplying the second integral; compare with Eq. (76), where Q*_1 is defined without the prefactor. This appears to be a typo and should be corrected.
  2. [Eq. (94c)] The displayed expression for κ_3 begins with 'κ3 = [d3/dλ3 h µ(h) I(λh)]', which looks like an editing remnant and should be replaced by the proper third derivative of μ(λ).
  3. [Eqs. (18)–(19)] The condition under which v_t(θ) reduces to the bare velocity θ is stated ambiguously ('or when it vanishes'); please spell out that the boundary densities are taken to zero in the rest of the paper and reconcile this with the nonzero n_± used in the partitioning protocol.
  4. [Fig. 4] The simulation details for inverting the mapping (4) and the binning procedure for the 10^8 trajectories are not given; adding this information would improve reproducibility.
  5. [Section 5] The final paragraph acknowledges overlap with Ref. [72] only in passing; the relation between the hard-rod correlation results obtained here and those of Ref. [72] should be discussed explicitly in the main text.
  6. [Eq. (113)] The derivative notation in the second source term, [∂_{Z'} q*_{τ_i}(Z', θ_i)]_{Z'=l*_i(θ_i)}, is easy to confuse with a derivative evaluated at a moving point; a parenthetical definition would help.

Circularity Check

0 steps flagged · score 2.0 of 10

No self-definitional or fitted-input circularity; the central derivation rests on an explicitly unproven initial-fluctuation ansatz, which is a correctness gap, not a circular reduction.

full rationale

I walked the derivation chain from Section 2 through Section 4. The point-particle BMFT is self-contained: the free-particle action (Eq. 35), saddle-point equations (Eqs. 40a-40d), and cumulant generating function (Eq. 44) are derived from the large-deviation functional in Eqs. (27)-(29), with no target result used as input. The interacting-system extension then uses the coordinate mapping (Eq. 14) and density relation (Eq. 16) to recast the observable as Eq. (58), and the action is again built from the same free-particle large-deviation functional (Eq. 61). The only system-specific input is the assumption that the mapped initial density r0 is governed by Eqs. (27)-(29); the paper states this explicitly: 'Here, we have assumed that the statistical nature of the initial profile, when described in the point particle density r_0(x, theta), is governed by the probability density functional with the large deviation function \~F[r_0] given in Eq. (27) along with Eq. (29). While a general proof is not available...' This is an unproven premise, not the output being fed back as input; the final FCS (Eq. 77) and two-point correlation (Eq. 123) are mathematically derived from it. The agreement checks against Refs. [24,25] (Eq. 95) and [70] (Eq. 126) are post-hoc benchmarks, not load-bearing inputs. Ref. [70] shares an author with the present paper, but it is used only as an independent comparison, and no fitted parameters or imported uniqueness theorems appear in the derivation. Hence there is no genuine circularity; the score of 2 reflects only minor, non-load-bearing self-citations in background and benchmarking while the central derivation retains independent mathematical content.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central derivation rests on two domain assumptions about integrable systems: the exactness of the point-particle mapping and the free-particle form of the initial fluctuation functional for generic models. The latter is explicitly stated as a conjecture. No free parameters are fitted, and no new entities are postulated.

assumptions (5)
  • domain assumption The wave-packet gas mapping x_i(t) = X_i(t) - 1/2 Σ_{k≠i} a(θ_i-θ_k) sgn(x_i(t)-x_k(t)) is exact for generic integrable models, with a(θ-θ') the two-body scattering shift.
    Invoked throughout (Eq. 4, Section 1.2 and Appendix A). This is the foundation for recasting the interacting problem in free-particle coordinates. Cited to the wave-packet gas literature (Refs. [45,64-67]).
  • ad hoc to paper Initial fluctuations of the mapped point-particle density r_0(X,θ) follow the free-particle large-deviation functional (Eqs. 27-29) for generic integrable models.
    Stated in Section 3 after Eq. (61). The authors note no general proof is available; only the hard-rods case is demonstrated in Appendix B.2. This is the paper's own conjecture and the weakest link.
  • standard math The saddle-point approximation of the path integral is valid for large observation time T.
    Used in Sections 2-4 to evaluate generating functions; standard in MFT and BMFT.
  • domain assumption The boundary densities vanish or are time-independent with zero net current, so the free-particle velocity is v_t(θ)=θ.
    Stated in Section 1.2 after Eq. (19); restricts to partitioning protocol and homogeneous setups with vacuum or undriven boundaries.
  • domain assumption The coordinate transformation (x,θ)->(X,k(θ)) is invertible with Jacobian given by Eq. (15).
    Needed to connect interacting and bare densities (Eqs. 15-16). Assumed for the wave-packet mapping, not proven in the paper.

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Cite this review

Pith. "Pith review of Ballistic macroscopic fluctuation theory via mapping to point particles." pith.science (2026). https://pith.science/paper/FLU5DIGX

@misc{pith2026250518093,
  author       = {Pith},
  title        = {Pith review of: Ballistic macroscopic fluctuation theory via mapping to point particles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FLU5DIGX}},
  note         = {Machine review of arXiv:2505.18093}
}
read the original abstract

Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for \emph{generic integrable models}, BMFT can be constructed through a direct mapping onto ensembles of classical or quantum point particles. This mapping generalises the well-known correspondence between hard spheres and point particles: the two-body \emph{scattering shift} now plays the role of an effective rod length for arbitrary interactions. Within this framework, we re-derive both the full-counting statistics and the long-range correlation functions previously obtained by other means, thereby providing a unified derivation. Our results corroborate the general picture that all late-time fluctuations and correlations stem from the initial noise, subsequently convected by Euler-scale hydrodynamics.

Figures

Figures reproduced from arXiv: 2505.18093 by the authors.

Figure 1
Figure 1. Cartoonish figure demonstrating the construction of the coordinates for a generic [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Schematic figure illustrating our modified BMFT approach for computing full [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Schematic plot of the (X, θ) phase space, partitioned into R strips of size ∆X which are labeled by index i ∈ {1, 2, ..., R} and centered around position Xi as shown by the pink strip. Each of these strips are further partitioned into M smaller subsystems of size ∆θ which are labeled by index (., j) and have particles with velocities between [θj − ∆θ/2, θj + ∆θ/2]. The subsystem labeled by (i, j) centered around (Xi… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Plot showing the rate function [Eq. (78) with ¯q0(Z, θ) given by Eq. (86)] for the density observable Q1 = Q˜ T /T, with h(θ) = 1, in a system of hard rods of length a = 1 4 and mean number of particles ⟨N⟩ = 214. Initial momenta are sampled from a Gaussian distributio…

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Reference graph

Works this paper leans on

71 extracted references · 39 canonical work pages · cited by 1 Pith paper

  1. [70]

    H¨ ubner, L

    F. H¨ ubner, L. Biagetti, J. D. Nardis and B. Doyon,Diffusive hydrodynamics of hard rods from microscopics(2025),arXiv:2503.07794

    arXiv 2025

  2. [1]

    Bertini, A

    L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim,Macro- scopic fluctuation theory, Reviews of Modern Physics87, 593 (2015), doi:10.1103/RevModPhys.87.593

    doi:10.1103/revmodphys.87.593 2015

  3. [2]

    Jona-Lasinio,Review article: Large fluctuations in non-equilibrium physics, Non- lin

    G. Jona-Lasinio,Review article: Large fluctuations in non-equilibrium physics, Non- lin. Processes Geophys.30, 253–262 (2023), doi:10.5194/npg-30-253-2023

    work page doi:10.5194/npg-30-253-2023 2023

  4. [3]

    Bertini, A

    L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim,Fluctuations in stationary nonequilibrium states of irreversible processes, Phys. Rev. Lett.87, 040601 (2001), doi:10.1103/PhysRevLett.87.040601

    doi:10.1103/physrevlett.87.040601 2001

  5. [4]

    Bertini, A

    L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim,Macroscopic fluctuation theory for stationary non-equilibrium states, J. Stat. Phys.107, 635–675 (2002), doi:10.1023/A:1014525911391

    doi:10.1023/a:1014525911391 2002

  6. [5]

    Derrida,Microscopic versus macroscopic approaches to non-equilibrium systems, J

    B. Derrida,Microscopic versus macroscopic approaches to non-equilibrium systems, J. Stat. Mech.2011, P01030 (2011), doi:10.1088/1742-5468/2011/01/P01030

    work page doi:10.1088/1742-5468/2011/01/p01030 2011

  7. [6]

    Tailleur, J

    J. Tailleur, J. Kurchan and V. Lecomte,Mapping out-of-equilibrium into equilibrium in one-dimensional transport models, J. Phys. A: Math. Theor.41, 505001 (2008), doi:10.1088/1751-8113/41/50/505001

    work page doi:10.1088/1751-8113/41/50/505001 2008

  8. [8]

    Saha and T

    S. Saha and T. Sadhu,Large deviations in the symmetric simple exclusion process with slow boundaries: A hydrodynamic perspective, SciPost Phys.17, 033 (2024), doi:10.21468/SciPostPhys.17.2.033

    work page doi:10.21468/scipostphys.17.2.033 2024

Show all 71 references
  1. [9]

    Bodineau and B

    T. Bodineau and B. Derrida,A perturbative approach to the macroscopic fluctuation theory, Journal of Statistical Physics192(4), 51 (2025), doi:10.1007/s10955-025- 03439-4

    2025 doi

  2. [10]

    Saha and T

    S. Saha and T. Sadhu,Large deviations of density in the non-equilibrium steady state of boundary-driven diffusive systems, arXiv preprint arXiv:2501.03164 (2025), doi:10.48550/arXiv.2501.03164

    2025 doi

  3. [11]

    Dandekar, P

    R. Dandekar, P. L. Krapivsky and K. Mallick,Current fluctuations in the dyson gas, Phys. Rev. E110, 064153 (2024), doi:10.1103/PhysRevE.110.064153

    2024 doi

  4. [12]

    Grabsch and O

    A. Grabsch and O. B´ enichou,Tracer diffusion beyond gaussian behavior: Ex- plicit results for general single-file systems, Phys. Rev. Lett.132, 217101 (2024), doi:10.1103/PhysRevLett.132.217101

    2024 doi

  5. [13]

    Mallick, H

    K. Mallick, H. Moriya and T. Sasamoto,Exact solutions to macroscopic fluctua- tion theory through classical integrable systems, J. Stat. Mech.2024, 074001 (2024), doi:10.1088/1742-5468/ad485e

    2024 doi

  6. [14]

    Sharma, S

    K. Sharma, S. Saha, S. Jangid and T. Sadhu,Large deviations of current for the symmetric simple exclusion process on a semi-infinite line and on an infinite line with a slow bond, arXiv preprint arXiv:2405.00654 (2024), doi:10.48550/arXiv.2405.00654. 29 SciPost Physics Submission

    2024 doi arXiv

  7. [15]

    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

  8. [16]

    Rana and T

    J. Rana and T. Sadhu,Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion, Phys. Rev. E107, L012101 (2023), doi:10.1103/PhysRevE.107.L012101

    2023 doi

  9. [17]

    Bettelheim, N

    E. Bettelheim, N. R. Smith and B. Meerson,Full statistics of nonstationary heat transfer in the kipnis–marchioro–presutti model, Journal of Statistical Mechanics: Theory and Experiment2022(9), 093103 (2022), doi:10.1088/1742-5468/ac7ae0

    2022 doi

  10. [18]

    Bernard,Can the macroscopic fluctuation theory be quantized?, Journal of Physics A: Mathematical and Theoretical54(43), 433001 (2021), doi:10.1088/1751- 8121/ac0f93

    D. Bernard,Can the macroscopic fluctuation theory be quantized?, Journal of Physics A: Mathematical and Theoretical54(43), 433001 (2021), doi:10.1088/1751- 8121/ac0f93

    2021 doi

  11. [19]

    Derrida and T

    B. Derrida and T. Sadhu,Large deviations conditioned on large deviations II: Fluc- tuating hydrodynamics, J. Stat. Phys.177, 151–182 (2019), doi:10.1007/s10955-019- 02363-8

    2019 doi

  12. [20]

    Sadhu and B

    T. Sadhu and B. Derrida,Correlations of the density and of the current in non- equilibrium diffusive systems, J. Stat. Mech.2016, 113202 (2016), doi:10.1088/1742- 5468/2016/11/113202

    2016 doi

  13. [21]

    P. L. Krapivsky, K. Mallick and T. Sadhu,Tagged particle in single-file diffusion, J. Stat. Phys.160, 885–925 (2015), doi:10.1007/s10955-015-1291-0

    2015 doi

  14. [22]

    P. L. Krapivsky, K. Mallick and T. Sadhu,Large deviations in single-file diffusion, Phys. Rev. Lett.113, 078101 (2014), doi:10.1103/PhysRevLett.113.078101

    2014 doi

  15. [23]

    Lecomte, A

    V. Lecomte, A. Imparato and F. van Wijland,Current fluctuations in systems with diffusive dynamics, in and out of equilibrium, Prog. Theor. Phys. Suppl.184, 276–289 (2010), doi:10.1143/PTPS.184.276

    2010 doi

  16. [24]

    Doyon, G

    B. Doyon, G. Perfetto, T. Sasamoto and T. Yoshimura,Emergence of hy- drodynamic spatial long-range correlations in nonequilibrium many-body systems, arXiv:2210.10009 (2022)

    2022 arXiv

  17. [25]

    Doyon, G

    B. Doyon, G. Perfetto, T. Sasamoto and T. Yoshimura,Ballistic macroscopic fluctu- ation theory, SciPost Phys.15, 136 (2023), doi:10.21468/SciPostPhys.15.4.136

    2023 doi

  18. [26]

    Yoshimura and i

    T. Yoshimura and i. c. v. Krajnik,Anomalous current fluctuations from euler hydro- dynamics, Phys. Rev. E111, 024141 (2025), doi:10.1103/PhysRevE.111.024141

    2025 doi

  19. [27]

    O. A. Castro-Alvaredo, B. Doyon and T. Yoshimura,Emergent hydrodynamics in integrable quantum systems out of equilibrium, Phys. Rev. X6, 041065 (2016), doi:10.1103/PhysRevX.6.041065

    2016 doi

  20. [28]

    Bertini, M

    B. Bertini, M. Collura, J. De Nardis and M. Fagotti,Transport in Out-of-Equilibrium XXZChains: Exact Profiles of Charges and Currents, Phys. Rev. Lett.117, 207201 (2016), doi:10.1103/PhysRevLett.117.207201

    2016 doi

  21. [29]

    Doyon, J

    B. Doyon, J. Dubail, R. Konik and T. Yoshimura,Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Su- persedes Conventional Hydrodynamics, Phys. Rev. Lett.119, 195301 (2017), doi:10.1103/PhysRevLett.119.195301. 30 SciPost Physics Submission

    2017 doi

  22. [30]

    De Nardis, D

    J. De Nardis, D. Bernard and B. Doyon,Hydrodynamic diffusion in integrable systems, Phys. Rev. Lett.121, 160603 (2018), doi:10.1103/PhysRevLett.121.160603

    2018 doi

  23. [31]

    J. D. Nardis, D. Bernard and B. Doyon,Diffusion in generalized hy- drodynamics and quasiparticle scattering, SciPost Phys.6, 49 (2019), doi:10.21468/SciPostPhys.6.4.049

    2019 doi

  24. [32]

    Doyon,Lecture Notes On Generalised Hydrodynamics, SciPost Phys

    B. Doyon,Lecture Notes On Generalised Hydrodynamics, SciPost Phys. Lect. Notes p. 18 (2020), doi:10.21468/SciPostPhysLectNotes.18

    2020 doi

  25. [33]

    Doyon and J

    B. Doyon and J. Durnin,Free energy fluxes and the kubo-martin-schwinger relation (2021),2007.09113

    2021 arXiv

  26. [34]

    Doyon and H

    B. Doyon and H. Spohn,Drude Weight for the Lieb-Liniger Bose Gas, SciPost Phys. 3, 039 (2017), doi:10.21468/SciPostPhys.3.6.039

    2017 doi

  27. [35]

    Doyon,Diffusion and superdiffusion from hydrodynamic projections, J

    B. Doyon,Diffusion and superdiffusion from hydrodynamic projections, J. Stat. Phys. 186(2), 25 (2022), doi:10.1007/s10955-021-02863-6

    2022 doi

  28. [36]

    Durnin, M

    J. Durnin, M. J. Bhaseen and B. Doyon,Nonequilibrium dynamics and weakly broken integrability, Phys. Rev. Lett.127, 130601 (2021), doi:10.1103/PhysRevLett.127.130601

    2021 doi

  29. [37]

    Doyon, H

    B. Doyon, H. Spohn and T. Yoshimura,A geometric viewpoint on generalized hydro- dynamics, Nucl. Phys. B926, 570 (2018), doi:10.1016/j.nuclphysb.2017.12.002

    2018 doi

  30. [38]

    Schemmer, I

    M. Schemmer, I. Bouchoule, B. Doyon and J. Dubail,Generalized hy- drodynamics on an atom chip, Phys. Rev. Lett.122, 090601 (2019), doi:10.1103/PhysRevLett.122.090601

    2019 doi

  31. [39]

    Bastianello, B

    A. Bastianello, B. Bertini, B. Doyon and R. Vasseur,Introduction to the special issue on emergent hydrodynamics in integrable many-body systems, J. Stat. Mech. Theory Exp.2022(1), 014001 (2022), doi:10.1088/1742-5468/ac3e6a

    2022 doi

  32. [40]

    F. S. Møller, G. Perfetto, B. Doyon and J. Schmiedmayer,Euler-scale dynamical correlations in integrable systems with fluid motion, SciPost Phys. Core3, 16 (2020), doi:10.21468/SciPostPhysCore.3.2.016

    2020 doi

  33. [41]

    Bastianello, B

    A. Bastianello, B. Doyon, G. Watts and T. Yoshimura,Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model, SciPost Phys.4, 45 (2018), doi:10.21468/SciPostPhys.4.6.045

    2018 doi

  34. [42]

    Bertini, F

    B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg and M. ˇZnidariˇ c,Finite-temperature transport in one-dimensional quantum lattice models, Rev. Mod. Phys.93, 025003 (2021), doi:10.1103/RevModPhys.93.025003

    2021 doi

  35. [43]

    Bastianello and A

    A. Bastianello and A. De Luca,Integrability-protected adiabatic reversibil- ity in quantum spin chains, Phys. Rev. Lett.122, 240606 (2019), doi:10.1103/PhysRevLett.122.240606

    2019 doi

  36. [44]

    V. B. Bulchandani, S. Gopalakrishnan and E. Ilievski,Superdiffusion in spin chains, J. Stat. Mech. Theory Exp.2021(8), 084001 (2021), doi:10.1088/1742-5468/ac12c7

    2021 doi

  37. [45]

    Doyon and F

    B. Doyon and F. H¨ ubner,Ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets, arXiv preprint arXiv:2307.09307 (2023), doi:10.48550/arXiv.2307.09307. 31 SciPost Physics Submission

    2023 doi arXiv

  38. [46]

    Møller, P

    F. Møller, P. Sch¨ uttelkopf, J. Schmiedmayer and S. Erne,Whitham ap- proach to generalized hydrodynamics, Phys. Rev. Res.6, 013328 (2024), doi:10.1103/PhysRevResearch.6.013328

    2024 doi

  39. [47]

    Malvania, Y

    N. Malvania, Y. Zhang, Y. Le, J. Dubail, M. Rigol and D. S. Weiss,Generalized hydrodynamics in strongly interacting 1d bose gases, Science373(6559), 1129 (2021), doi:DOI: 10.1126/science.abf0147

    2021 doi

  40. [48]

    Ruggiero, P

    P. Ruggiero, P. Calabrese, B. Doyon and J. Dubail,Quantum generalized hydrody- namics, Phys. Rev. Lett.124, 140603 (2020), doi:10.1103/PhysRevLett.124.140603

    2020 doi

  41. [49]

    Møller, N

    F. Møller, N. Besse, I. E. Mazets, H.-P. Stimming and N. J. Mauser,The dissipa- tive Generalized Hydrodynamic equations and their numerical solution, Journal of Computational Physics493, 112431 (2023), doi:10.1016/j.jcp.2023.112431

    2023

  42. [50]

    V. B. Bulchandani, R. Vasseur, C. Karrasch and J. E. Moore,Bethe–Boltzmann hydrodynamics and spin transport in the XXZ chain, Phys. Rev. B97(4), 045407 (2018), doi:10.1103/PhysRevB.97.045407

    2018 doi

  43. [51]

    Møller, S

    F. Møller, S. Erne, N. J. Mauser, J. Schmiedmayer and I. E. Mazets,Bridging Effective Field Theories and Generalized Hydrodynamics, arXiv preprint arXiv:2205.15871 (2022),2205.15871

    2022 arXiv

  44. [52]

    Bastianello, V

    A. Bastianello, V. Alba and J.-S. Caux,Generalized hydrodynamics with space-time inhomogeneous interactions, Phys. Rev. Lett.123, 130602 (2019), doi:10.1103/PhysRevLett.123.130602

    2019 doi

  45. [53]

    Møller, B

    F. Møller, B. C. Nagy, M. Kormos and G. Tak´ acs,Anomalous charge transport in the sine–Gordon model, arXiv preprint arXiv:2411.11473 (2024),2411.11473

    2024

  46. [54]

    Doyon, S

    B. Doyon, S. Gopalakrishnan, F. Møller, J. Schmiedmayer and R. Vasseur,Gen- eralized Hydrodynamics: A Perspective, Phys. Rev. X15(1), 010501 (2025), doi:10.1103/PhysRevX.15.010501

    2025 doi

  47. [55]

    Bonnemain, B

    T. Bonnemain, B. Doyon and G. El,Generalized hydrodynamics of the kdv soliton gas, Journal of Physics A: Mathematical and Theoretical55(37), 374004 (2022), doi:10.1088/1751-8121/ac8253

    2022 doi

  48. [56]

    Bastianello, i

    A. Bastianello, i. c. v. Krajnik and E. Ilievski,Landau-lifschitz magnets: Exact thermodynamics and transport, Phys. Rev. Lett.133, 107102 (2024), doi:10.1103/PhysRevLett.133.107102

    2024 doi

  49. [57]

    Gopalakrishnan, A

    S. Gopalakrishnan, A. Morningstar, R. Vasseur and V. Khemani,Theory of anoma- lous full counting statistics in anisotropic spin chains, arXiv:2203.09526 (2022)

    2022 arXiv

  50. [58]

    Gopalakrishnan, E

    S. Gopalakrishnan, E. McCulloch and R. Vasseur,Non-gaussian diffusive fluctuations in dirac fluids, Proceedings of the National Academy of Sciences121(50) (2024), doi:10.1073/pnas.2403327121

    2024 doi

  51. [60]

    Krajnik, J

    v. Krajnik, J. Schmidt, V. Pasquier, E. Ilievski and T. Prosen,Exact anomalous current fluctuations in a deterministic interacting model, Physical Review Letters 128(16) (2022), doi:10.1103/physrevlett.128.160601. 32 SciPost Physics Submission

    2022 doi

  52. [61]

    McCulloch, R

    E. McCulloch, R. Vasseur and S. Gopalakrishnan,Ballistic modes as a source of anomalous charge noise, Phys. Rev. E111, 015410 (2025), doi:10.1103/PhysRevE.111.015410

    2025 doi

  53. [62]

    Spohn,Large Scale Dynamics of Interacting Particles, Springer Berlin Heidelberg, doi:10.1007/978-3-642-84371-6 (1991)

    H. Spohn,Large Scale Dynamics of Interacting Particles, Springer Berlin Heidelberg, doi:10.1007/978-3-642-84371-6 (1991)

    1991 doi

  54. [63]

    P. A. Ferrari and S. Olla,Macroscopic diffusive fluctuations for generalized hard rods dynamics, arXiv preprint arXiv:2305.13037 (2023), doi:10.48550/arXiv.2305.13037

    2023 doi arXiv

  55. [64]

    Doyon, F

    B. Doyon, F. H¨ ubner and T. Yoshimura,New classical integrable sys- tems from generalizedt T-deformations, Phys. Rev. Lett.132, 251602 (2024), doi:10.1103/PhysRevLett.132.251602

    2024 doi

  56. [65]

    Doyon, J

    B. Doyon, J. Durnin and T. Yoshimura,The Space of Integrable Sys- tems from GeneralisedT ¯T-Deformations, SciPost Phys.13, 072 (2022), doi:10.21468/SciPostPhys.13.3.072

    2022 doi

  57. [66]

    Bonnemain, V

    T. Bonnemain, V. Caudrelier and B. Doyon,Hamiltonian formulation and as- pects of integrability of generalised hydrodynamics, Annales Henri Poincar´ e (2025), doi:10.1007/s00023-025-01546-2

    2025 doi

  58. [67]

    Aggarwal,Asymptotic scattering relation for the toda lattice, arXiv preprint arXiv:2503.08018 (2025), doi:10.48550/arXiv.2503.08018

    A. Aggarwal,Asymptotic scattering relation for the toda lattice, arXiv preprint arXiv:2503.08018 (2025), doi:10.48550/arXiv.2503.08018

    2025 doi arXiv

  59. [68]

    Gopalakrishnan, D

    S. Gopalakrishnan, D. A. Huse, V. Khemani and R. Vasseur,Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems, Phys. Rev. B98, 220303 (2018), doi:10.1103/PhysRevB.98.220303

    2018 doi

  60. [69]

    H¨ ubner, L

    F. H¨ ubner, L. Biagetti, J. De Nardis and B. Doyon,Diffusive hydrody- namics from long-range correlations, Phys. Rev. Lett.134, 187101 (2025), doi:10.1103/PhysRevLett.134.187101

    2025 doi

  61. [71]

    Piroli, J

    L. Piroli, J. De Nardis, M. Collura, B. Bertini and M. Fagotti,Transport in out-of- equilibrium xxz chains: Nonballistic behavior and correlation functions, Phys. Rev. B 96, 115124 (2017), doi:10.1103/PhysRevB.96.115124

    2017 doi

  62. [72]

    Kundu,Macroscopic fluctuation theory of correlations in hard rod gas, arXiv preprint arXiv:2504.09201 (2025), doi:https://doi.org/10.48550/arXiv.2504.09201

    A. Kundu,Macroscopic fluctuation theory of correlations in hard rod gas, arXiv preprint arXiv:2504.09201 (2025), doi:https://doi.org/10.48550/arXiv.2504.09201

    2025 doi

  63. [73]

    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. Theory Exp.2007(07), P07023 (2007), doi:10.1088/1742-5468/2007/07/p07023. 33

    2007 doi

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