Non-equilibrium Fluctuations of Interacting Particle Systems

TL;DR

This paper studies the large-scale fluctuation behavior of weakly asymmetric exclusion processes in up to three dimensions, providing new entropy estimates and convergence bounds for the hydrodynamic limit.

Contribution

It introduces a sharp entropy estimate applicable in any dimension, advancing understanding of non-equilibrium fluctuations in interacting particle systems.

Findings

Derived the large-scale fluctuation limit in 3D

Established entropy bounds for the process law

Provided quantitative convergence rates to hydrodynamics

Abstract

We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative entropy of the law of the process with respect to product reference measures associated to the hydrodynamic limit profile, which holds in any dimension and is of independent interest. As a corollary of this entropy estimate, we obtain some quantitative bounds on the speed of convergence of the aforementioned hydrodynamic limit.