Exclusion processes with non-reversible boundary: hydrodynamics and large deviations

TL;DR

This paper studies a one-dimensional exclusion process with non-reversible boundary conditions, deriving the hydrodynamic limit as a heat equation with nonlinear Robin boundary conditions and establishing a large deviations principle.

Contribution

It provides a rigorous derivation of hydrodynamics and large deviations for exclusion processes with non-reversible boundary interactions, highlighting multiple stationary solutions.

Findings

Hydrodynamic limit described by heat equation with nonlinear Robin boundary conditions

Existence of multiple stationary solutions for certain boundary rates

Established a dynamical large deviations principle

Abstract

We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For appropriate choices of the boundary rates, these partial differential equations have more than one stationary solution. We prove the dynamical large deviations principle.