The gradient flow approach to hydrodynamic limits for the simple exclusion process

TL;DR

This paper introduces a novel gradient flow-based method to analyze the hydrodynamic limit of the symmetric simple exclusion process, connecting particle system behavior to the heat equation.

Contribution

It provides a new approach to derive hydrodynamic limits by leveraging the gradient flow structure of the particle system.

Findings

Characterizes limits of empirical density measures as solutions to the heat equation

Establishes a gradient flow framework for the SSEP

Offers a new perspective on hydrodynamic limit derivation

Abstract

We give a new approach to the well-known convergence to the hydrodynamic limit for the symmetric simple exclusion process (SSEP). More precisely, we characterize any possible limit of its empirical density measures as solutions to the heat equation by passing to the limit in the gradient flow structure of the particle system.