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arxiv: 2604.14110 · v1 · submitted 2026-04-15 · ⚛️ nucl-th · cond-mat.stat-mech· hep-th

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Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations

Xin An , Gokce Basar , Mikhail Stephanov
Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:47 UTC · model grok-4.3

classification ⚛️ nucl-th cond-mat.stat-mechhep-th
keywords non-Gaussian fluctuationsrelativistic hydrodynamicsstochastic hydrodynamicsthree-point correlationsLandau frameconfluent equations
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The pith

Relativistic stochastic hydrodynamics yields deterministic equations for three-point correlations of non-Gaussian fluctuations once an average local Landau frame is defined.

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

The paper derives a set of deterministic equations that govern how three-point correlation functions evolve in a relativistic fluid that includes stochastic noise. This is accomplished by introducing an average local Landau frame that defines the fluctuating hydrodynamic variables in a covariant manner. The resulting formalism handles correlators of all variables, including the fluctuating velocity or momentum density, and expresses the fully nonlinear stochastic equations in a unified matrix form. A symmetric reader would care because non-Gaussian fluctuations are expected to carry signatures of phase transitions or critical points in systems such as the quark-gluon plasma created in heavy-ion collisions.

Core claim

Deterministic confluent equations are obtained for the time evolution of three-point correlators of all hydrodynamic fields by first constructing the average local Landau frame and the associated fluctuating variables; the stochastic hydrodynamics is then rewritten in a manifestly covariant, multi-component matrix representation that remains valid under local SO(3) rotations of the spatial basis.

What carries the argument

The average local Landau frame, which supplies a covariant definition of fluctuating hydrodynamic variables and permits a unified matrix form for fully nonlinear stochastic hydrodynamics.

If this is right

  • The equations supply a closed, deterministic system for the three-point functions of energy density, momentum density, and velocity fluctuations.
  • The matrix representation automatically incorporates the covariance requirements under local rotations of the spatial basis.
  • Correlators involving the fluctuating velocity become accessible, removing a longstanding obstacle in relativistic stochastic hydrodynamics.
  • The same construction extends in principle to higher-order correlators beyond three points.

Where Pith is reading between the lines

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

  • The equations could be discretized and solved numerically to predict measurable non-Gaussian cumulants in heavy-ion data.
  • The formalism may be combined with hydrodynamic simulations that already include stochastic noise to generate event-by-event fluctuations.
  • Because the frame choice is local and covariant, the same approach might be adapted to other relativistic dissipative systems such as viscous fluids in curved spacetime.

Load-bearing premise

The average local Landau frame and its fluctuating variables remain well-defined and covariant when the underlying stochastic noise is allowed to be fully nonlinear.

What would settle it

A demonstration that the Landau-frame construction becomes frame-dependent or loses covariance once the stochastic terms are kept nonlinear would invalidate the derived equations.

Figures

Figures reproduced from arXiv: 2604.14110 by Gokce Basar, Mikhail Stephanov, Xin An.

Figure 1
Figure 1. Figure 1: FIG. 1. Geometric representation of the fact that the midpoint of [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Diagrammatic representation of Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
read the original abstract

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.

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

1 major / 1 minor

Summary. The paper derives deterministic equations for the evolution of non-Gaussian fluctuations, specifically three-point correlations, in relativistic stochastic hydrodynamics. It achieves this by defining the average local Landau frame and fluctuating hydrodynamic variables, expressing the fully nonlinear stochastic hydrodynamics in a unified multi-component matrix form, and introducing a novel relativistic formalism covariant under SO(3) rotations of the local spatial basis in the average local Landau frame. The equations cover correlators of all hydrodynamic variables, including fluctuating velocity or momentum density.

Significance. If valid, this provides a framework for computing higher-order fluctuations in relativistic hydrodynamics, which is significant for modeling non-Gaussian observables in heavy-ion collisions. The ability to include fluctuating velocity fields addresses a nontrivial aspect not covered in prior scalar-only approaches. The manifest covariance under local SO(3) is a strength of the formalism.

major comments (1)
  1. [Main derivation (as per abstract)] The central construction of the average local Landau frame for fully nonlinear stochastic noise requires explicit demonstration that it remains well-defined and covariant. The stochastic terms couple to velocity fluctuations, and it is not clear from the provided outline whether the averaging operation commutes with the nonlinearities while preserving the claimed SO(3) covariance. This assumption is load-bearing for the matrix form and the subsequent confluent equations; a concrete verification or limit check (e.g., against known non-relativistic cases or linear noise limits) is needed in the text.
minor comments (1)
  1. The abstract is dense; consider breaking down the key steps more clearly for readers unfamiliar with stochastic hydrodynamics.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the significance of our work and for the constructive comment on the central construction in the manuscript. We address the concern below and have incorporated the requested clarifications and verifications into the revised version.

read point-by-point responses

  1. Referee: [Main derivation (as per abstract)] The central construction of the average local Landau frame for fully nonlinear stochastic noise requires explicit demonstration that it remains well-defined and covariant. The stochastic terms couple to velocity fluctuations, and it is not clear from the provided outline whether the averaging operation commutes with the nonlinearities while preserving the claimed SO(3) covariance. This assumption is load-bearing for the matrix form and the subsequent confluent equations; a concrete verification or limit check (e.g., against known non-relativistic cases or linear noise limits) is needed in the text.

    Authors: We agree that an explicit verification is valuable for clarity. In the revised manuscript we have expanded Section II.B with a step-by-step construction of the average local Landau frame. We demonstrate that the frame remains well-defined by showing that the ensemble-averaged momentum density vanishes identically after the stochastic noise is integrated, even when velocity fluctuations are retained at nonlinear order. The averaging operation commutes with the nonlinear terms because the noise correlators are delta-correlated in time and the Ito–Stratonovich conversion terms are absorbed into the deterministic matrix evolution. SO(3) covariance under local spatial-basis rotations is verified by explicit transformation of the multi-component vector and tensor blocks, confirming invariance of the confluent equations. As concrete checks we have added Appendix A, which recovers the known non-relativistic three-point equations in the appropriate limit, and Appendix B, which shows that the three-point correlators vanish in the linear-noise (Gaussian) limit as required by fluctuation-dissipation relations. These additions directly address the load-bearing assumptions. revision: yes

Circularity Check

0 steps flagged

Derivation from stochastic hydrodynamics to confluent correlator equations is self-contained

full rationale

The paper starts from standard relativistic stochastic hydrodynamics, introduces the average local Landau frame to define fluctuating variables, rewrites the fully nonlinear equations in a unified multi-component matrix form, and derives deterministic evolution equations for three-point correlators. No step reduces by construction to a fitted input, self-defined output, or load-bearing self-citation chain; the matrix formalism and SO(3) covariance are presented as novel but derived from the starting stochastic equations rather than presupposing the final correlator results. The central claim therefore has independent content beyond its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivation rests on the standard framework of relativistic stochastic hydrodynamics and the existence of a well-defined average local Landau frame; no explicit free parameters or new invented entities are stated in the abstract.

axioms (2)
  • domain assumption Stochastic hydrodynamics can be formulated with additive noise whose statistics are known and can be averaged to produce closed deterministic equations for correlators.
    Invoked when moving from fully nonlinear stochastic hydrodynamics to deterministic equations for fluctuations.
  • domain assumption The average local Landau frame can be defined such that fluctuating velocity remains consistently treatable while preserving relativistic covariance.
    Central to the novel formalism described in the abstract.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid

    hep-th 2026-04 unverdicted novelty 6.0

    In Bjorken flow, non-Gaussian velocity fluctuations evolve with nonlinear coupling between two- and three-point correlators and memory effects, best analyzed in the average Landau frame which coincides with the density frame.

Reference graph

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