Dynamical large deviations for the boundary driven weakly asymmetric exclusion process

TL;DR

This paper establishes a large deviations principle for the boundary driven weakly asymmetric exclusion process, linking microscopic particle dynamics to macroscopic hydrodynamic behavior described by the viscous Burgers equation.

Contribution

It provides the first rigorous proof of dynamical large deviations for this class of boundary-driven exclusion processes, connecting microscopic models to macroscopic fluctuation theory.

Findings

Hydrodynamic limit described by viscous Burgers equation with boundary conditions

Dynamical large deviations principle proven for the process

Bridges microscopic particle behavior with macroscopic fluctuation analysis

Abstract

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. We prove the associated dynamical large deviations principle.