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arxiv: 2512.15569 · v2 · pith:M6BTR5LJnew · submitted 2025-12-17 · ❄️ cond-mat.stat-mech

Macroscopic fluctuation theory of interacting Brownian particles

Aur\'elien Grabsch , Davide Venturelli , Olivier B\'enichou This is my paper

Pith reviewed 2026-05-21 16:44 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords macroscopic fluctuation theoryinteracting Brownian particlescollective diffusion coefficientdensity-current correlationssingle-file diffusionCalogero gasRiesz gasvirial expansion
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The pith

Macroscopic fluctuation theory combined with equilibrium collective diffusion gives exact large-scale dynamics for interacting Brownian particles.

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

This paper applies macroscopic fluctuation theory to Brownian particles with arbitrary pairwise interactions. By using the collective diffusion coefficient from equilibrium statistical mechanics, they derive exact large-scale dynamical properties both in and out of equilibrium, focusing on density and current correlations. This provides precise results for one-dimensional models like the Calogero and Riesz gases as well as for systems with nearest-neighbor interactions. Tracer diffusion under single-file constraints is also analyzed for arbitrary interactions, while higher-dimensional cases are treated with virial expansions.

Core claim

By combining it with standard results of equilibrium statistical mechanics for the collective diffusion coefficient, the MFT gives access to the exact large-scale dynamical properties of the system, both in- and out-of-equilibrium. In particular, we obtain exact results for dynamical correlations between the density and the current of particles.

What carries the argument

Macroscopic fluctuation theory framework incorporating the collective diffusion coefficient from equilibrium statistical mechanics to capture interaction effects at large scales.

If this is right

  • Exact results for dynamical correlations between the density and the current of particles in and out of equilibrium.
  • Precise description of these correlations for one-dimensional models such as the Calogero and Riesz gases and nearest-neighbor interaction systems.
  • Characterization of tracer diffusion with the single-file constraint for arbitrary pairwise interactions.
  • Quantitative results for higher-dimensional systems using virial expansion methods.

Where Pith is reading between the lines

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

  • The framework may enable similar exact results for other dynamical quantities in interacting particle systems where equilibrium coefficients are known.
  • It suggests a general way to bridge equilibrium statistical mechanics with non-equilibrium fluctuation theories for transport calculations.
  • Potential applications include modeling of fluctuations in colloidal suspensions or other many-body systems with pairwise forces.

Load-bearing premise

The collective diffusion coefficient obtained from equilibrium statistical mechanics can be inserted directly into the macroscopic fluctuation theory framework for arbitrary pairwise interactions without additional out-of-equilibrium corrections or validity restrictions.

What would settle it

Comparison of the predicted dynamical correlations with results from direct numerical simulations of the particle trajectories in a specific model, such as the Riesz gas or tethered particles.

Figures

Figures reproduced from arXiv: 2512.15569 by Aur\'elien Grabsch, Davide Venturelli, Olivier B\'enichou.

Figure 1
Figure 1. Figure 1: FIG. 1. Diffusion coefficient [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Diffusion coefficient for the Rouse chain with nearest-neighbour interaction potential ( [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Prefactor of the asymptotic behaviour of [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Prefactor of the asymptotic behaviour of (a) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic representation of interacting Brownian [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scaled correlation profile [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the collective diffusion coefficient, the MFT gives access to the exact large-scale dynamical properties of the system, both in- and out-of-equilibrium. In particular, we obtain exact results for dynamical correlations between the density and the current of particles. For one-dimensional systems, this allows us to obtain a precise description of these correlations for emblematic models, such as the Calogero and Riesz gases, and for systems with nearest-neighbor interactions such as the Rouse chain of hardcore particles or the recently introduced model of tethered particles. Tracer diffusion with the single-file constraint (but for arbitrary pairwise interaction) is also studied. For higher-dimensional systems, we quantitatively characterize these dynamical correlations by relying on standard methods such as the virial expansion.

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 / 2 minor

Summary. The paper applies macroscopic fluctuation theory (MFT) to Brownian particles with arbitrary pairwise interactions. It combines MFT with the collective diffusion coefficient from equilibrium statistical mechanics to claim exact access to large-scale dynamical properties in and out of equilibrium, particularly dynamical correlations between density and current. Applications include 1D models like Calogero and Riesz gases, Rouse chain, tethered particles, single-file tracer diffusion, and higher-D via virial expansion.

Significance. If the results hold, this provides a valuable framework for obtaining exact dynamical correlations in interacting particle systems without additional parameters, extending MFT to general interactions and enabling precise descriptions for important models in statistical mechanics. The approach could be useful for both theoretical understanding and quantitative characterization of non-equilibrium dynamics.

major comments (1)
  1. The central claim relies on direct insertion of the equilibrium collective diffusion coefficient D(ρ) into the MFT equations to obtain exact out-of-equilibrium density-current correlations for arbitrary pairwise potentials. No explicit derivation is supplied demonstrating that higher-order gradient corrections or interaction-induced memory effects vanish in the hydrodynamic limit (e.g., for Calogero 1/r² or Riesz 1/r^α potentials). This justification is load-bearing for the exactness assertion both in and out of equilibrium.
minor comments (2)
  1. The abstract and introduction could more clearly delineate which results follow from the MFT-equilibrium combination versus standard hydrodynamic limits.
  2. For the 1D applications, additional references to prior exact solutions for Calogero and Riesz gases would strengthen the context.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for their positive evaluation of its significance. We address the single major comment below.

read point-by-point responses

  1. Referee: The central claim relies on direct insertion of the equilibrium collective diffusion coefficient D(ρ) into the MFT equations to obtain exact out-of-equilibrium density-current correlations for arbitrary pairwise potentials. No explicit derivation is supplied demonstrating that higher-order gradient corrections or interaction-induced memory effects vanish in the hydrodynamic limit (e.g., for Calogero 1/r² or Riesz 1/r^α potentials). This justification is load-bearing for the exactness assertion both in and out of equilibrium.

    Authors: We thank the referee for highlighting this point. Macroscopic fluctuation theory is constructed precisely in the hydrodynamic scaling limit, where fields are coarse-grained over lengths much larger than any microscopic scale (particle size or interaction range). In this regime, higher-order gradient corrections are systematically suppressed by powers of the inverse macroscopic length and do not contribute to the leading large-scale correlations. The underlying microscopic dynamics are overdamped Langevin equations, which are Markovian; consequently, no interaction-induced memory kernels survive at the hydrodynamic level. The equilibrium collective diffusion coefficient D(ρ) is obtained from the static structure factor (or equivalently from the second derivative of the free-energy functional) and already encodes the full effect of arbitrary pairwise interactions on the equilibrium fluctuations. Inserting this D(ρ) into the MFT action therefore yields the exact leading-order dynamical correlations without additional parameters. For the long-range cases (Calogero 1/r² and Riesz 1/r^α), the same hydrodynamic argument applies once D(ρ) is computed from the known equilibrium thermodynamics of these models. We will add a concise paragraph in Section II (or a short appendix) that recalls the standard hydrodynamic derivation of MFT for interacting Brownian particles and explicitly states why higher-order and memory corrections are negligible. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation combines independent equilibrium inputs with MFT framework

full rationale

The paper applies the macroscopic fluctuation theory (MFT) to Brownian particles with arbitrary pairwise interactions and inserts the collective diffusion coefficient D(ρ) obtained from standard equilibrium statistical mechanics. This step is presented as yielding exact large-scale dynamical properties and density-current correlations both in and out of equilibrium, including for models such as the Calogero gas and Riesz gas. No quoted equation or derivation step reduces a prediction to a fitted parameter or self-citation by construction; the equilibrium results are invoked as external, independent inputs rather than derived within the paper. The framework for one- and higher-dimensional cases relies on this combination without evidence that out-of-equilibrium results are tautologically forced by the inputs. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of macroscopic fluctuation theory to interacting Brownian particles and on the direct usability of pre-existing equilibrium collective diffusion coefficients; no new free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Macroscopic fluctuation theory applies to systems of Brownian particles with arbitrary pairwise interactions.
    Invoked as the foundational framework for deriving dynamical properties.
  • domain assumption Equilibrium statistical mechanics supplies the exact collective diffusion coefficient that can be combined with MFT.
    Used directly to obtain both in- and out-of-equilibrium results.

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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. Universal tracer statistics in single-file transport

    cond-mat.stat-mech 2026-04 unverdicted novelty 7.0

    Tracer position statistics in single-file hard-rod transport are universal across diffusive and ballistic dynamics for one-time distributions.

Reference graph

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106 extracted references · 106 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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