Static large deviations for a reaction-diffusion model

TL;DR

This paper establishes a large deviations principle for a reaction-diffusion model combining exclusion and spin-flip dynamics, showing the stationary state concentrates on stable hydrodynamic solutions.

Contribution

It proves the large deviations principle for the empirical measure of a reaction-diffusion system with combined dynamics, linking microscopic behavior to macroscopic stability.

Findings

Large deviations principle for the empirical measure in the model

Stationary state concentrates on stable hydrodynamic solutions

Identification of stable solutions of the hydrodynamic equation

Abstract

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical measure under the stationary state. We deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable.