Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions

TL;DR

This paper establishes a large deviations principle for the empirical measure of a symmetric exclusion process with Robin boundary conditions, connecting microscopic dynamics to macroscopic heat equation behavior.

Contribution

It introduces a dynamical large deviations framework for the symmetric exclusion process with Robin boundary conditions, extending previous models with new boundary interaction analysis.

Findings

Proves the large deviations principle for the process

Connects microscopic dynamics to the heat equation with Robin boundaries

Extends large deviations theory to boundary-driven exclusion processes

Abstract

In this article, we consider a one-dimensional symmetric exclusion process in weak contact with reservoirs at the boundary. In the diffusive time-scaling the empirical measure evolves according to the heat equation with Robin boundary conditions. We prove the associated dynamical large deviations principle.