Quasi-Static Large Deviations

TL;DR

This paper investigates large deviations in a symmetric exclusion process with slowly varying boundary conditions, deriving explicit large deviation functionals and establishing fluctuation relations for the density and current.

Contribution

It provides a detailed analysis of large deviations in a quasi-static hydrodynamic limit, including explicit functional forms and fluctuation relations, extending previous hydrodynamic results.

Findings

Explicit large deviation functional identified

Fluctuation relation proven for the system

Analysis of density field and total current deviations

Abstract

We consider the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system reaches the stationary state.This gives rise to the quasi static hydrodynamic limit proven in [10]. We study here the large deviations with respect to this limit for the particle density field and the total current. We identify explicitely the large deviation functional and prove that it satisfies a fluctuation relation.