Macroscopic fluctuation theory of interacting Brownian particles

TL;DR

This paper applies macroscopic fluctuation theory to analyze large-scale dynamical properties of interacting Brownian particles, providing exact results for correlations and extending to various models and dimensions.

Contribution

It combines MFT with equilibrium statistical mechanics to derive exact large-scale dynamical properties for systems with arbitrary pairwise interactions.

Findings

Exact dynamical correlations between density and current are obtained.

Precise descriptions for models like Calogero and Riesz gases are provided.

Dynamical correlations are quantitatively characterized in higher dimensions.

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.