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arxiv: 2604.27730 · v1 · submitted 2026-04-30 · ✦ hep-th · nucl-th

Recognition: unknown

Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid

Gokce Basar , Shuo Song
Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:54 UTC · model grok-4.3

classification ✦ hep-th nucl-th
keywords non-Gaussian fluctuationshydrodynamic fluctuationsBjorken flowrelativistic hydrodynamicsvelocity correlatorsQCD critical pointeffective field theorymemory effects
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0 comments X

The pith

In boost-invariant relativistic expansion, non-Gaussian velocity fluctuations obey solvable equations in the average Landau frame, with three-point correlators showing nonlinear memory effects.

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

The paper sets out to derive how velocity fluctuations beyond Gaussian statistics evolve in a fluid that expands in a boost-invariant manner. It presents evolution equations for the two- and three-point correlation functions of these fluctuations and solves them analytically. The work shows that the average Landau frame provides a convenient description when relativistic effects matter, and that in this frame the three-point functions depend on the past history of the two-point functions in a nonlinear way. This matters for interpreting fluctuation measurements in heavy-ion collisions aimed at locating the QCD critical point, where non-Gaussian signals are expected to be enhanced.

Core claim

Using the effective field theory framework, the evolution equations for two- and three-point velocity correlators are derived for a hydrodynamic system in Bjorken flow. Analytical solutions are obtained, and the average Landau frame is identified as better suited for studying non-Gaussian fluctuations of velocity in the presence of relativistic effects; in the Bjorken background this frame corresponds to the density frame. The three-point correlators depend nonlinearly on the non-equilibrium dynamics of the two-point functions and display memory effects.

What carries the argument

The average Landau frame, which in Bjorken flow coincides with the density frame and allows the derivation of closed, analytically solvable equations for the velocity correlators.

Load-bearing premise

The effective field theory framework for fluctuating hydrodynamics remains accurate throughout the entire expansion for describing non-Gaussian velocity fluctuations.

What would settle it

A numerical simulation or experimental observation in a Bjorken-like expanding system where the three-point velocity correlators do not display the predicted nonlinear dependence on the two-point function dynamics.

Figures

Figures reproduced from arXiv: 2604.27730 by Gokce Basar, Shuo Song.

Figure 1
Figure 1. Figure 1: FIG. 1. The three-point correlator (normalized to be dimensionless) of transverse momentum fluctuations for two different view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The two-point correlator (normalized to its equilibrium value) fluctuations for two different values of view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The ratio of the three-point correlator to the late time expansion given in Eq. (4.22) up to NNLO. view at source ↗
read the original abstract

We consider non-equilibrium evolution of non-Gaussian fluctuations in a hydrodynamic system undergoing a boost-invariant expansion described by Bjorken flow. We derive the evolution equations for two- and three-point velocity correlators using the effective field theory framework and present analytical solutions for them. We show that the average Landau frame is better suited for studying non-Gaussian fluctuations of velocity when relativistic effects are important. In the Bjorken background, the average Landau frame corresponds to the density frame. We demonstrate that the three-point correlators depend nonlinearly on the non-equilibrium dynamics of the two-point functions, and exhibit non-trivial effects such as memory. The importance of these effects in the context of the search for the QCD critical point via fluctuations is discussed.

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

0 major / 4 minor

Summary. The manuscript derives the evolution equations for two- and three-point velocity correlators in a boost-invariant relativistic fluid undergoing Bjorken flow within the effective field theory framework for fluctuating hydrodynamics. It supplies closed-form analytical solutions, demonstrates that the average Landau frame reduces to the density frame for this background and is preferable when relativistic effects matter, and shows that the three-point correlators depend nonlinearly on the two-point dynamics with memory integrals. The relevance of these results to searches for the QCD critical point is discussed as an application.

Significance. If the derivations and solutions hold, the work supplies exact analytical results for non-Gaussian fluctuations in an expanding relativistic system, a rare achievement in this area where most treatments are numerical. The explicit treatment of frame choice, the nonlinear coupling between correlators, and the memory effects provide concrete, parameter-free insights that can inform both future simulations and phenomenological modeling of fluctuations in heavy-ion collisions. The clean derivation with no free parameters or ad-hoc entities is a notable strength.

minor comments (4)
  1. The introduction would benefit from a short paragraph contrasting the present non-Gaussian treatment with earlier Gaussian-fluctuation studies in Bjorken flow to clarify the incremental advance.
  2. In the section presenting the analytical solutions, the memory integral appearing in the three-point correlator could be accompanied by a brief physical interpretation of its origin from the nonlinear coupling to the two-point dynamics.
  3. The discussion of implications for QCD critical-point searches remains qualitative; adding one concrete example of how the memory or nonlinear effects would modify a measurable cumulant ratio would strengthen the phenomenological section.
  4. Notation for the velocity correlators (e.g., the precise definition of the average Landau frame velocity) should be collected in a single early subsection for easier reference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The report highlights the value of our analytical results on non-Gaussian fluctuations in Bjorken flow, including the frame choice and nonlinear coupling. No specific major comments were provided, so we interpret the recommendation as calling for minor improvements in presentation or clarity. We will revise the manuscript accordingly.

Circularity Check

0 steps flagged

Derivation self-contained from standard EFT; no circular reductions

full rationale

The manuscript begins from the established effective field theory of fluctuating relativistic hydrodynamics, writes the stochastic equations for velocity fluctuations on a Bjorken background, and derives the closed evolution equations for the two- and three-point correlators by direct expansion and averaging. The analytical solutions are obtained by solving the resulting linear integro-differential system exactly; the average-Landau-frame redefinition is shown by explicit coordinate transformation to coincide with the density frame for this flow. No fitted parameters are relabeled as predictions, no self-citation supplies a uniqueness theorem or ansatz that the present work then treats as external, and the three-point memory integrals arise directly from the nonlinear coupling to the two-point dynamics rather than by construction. The construction is therefore independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, no specific free parameters, axioms, or invented entities are detailed. The work relies on the effective field theory framework for hydrodynamics, which is standard in the field.

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Reference graph

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