Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

TL;DR

This paper studies the non-equilibrium and stationary fluctuations of a symmetric exclusion process with slowed boundary reservoirs, revealing detailed fluctuation behaviors under specific boundary conditions.

Contribution

It provides a rigorous analysis of fluctuation phenomena in a symmetric exclusion process with boundary rates scaled by 1/n, extending understanding of non-equilibrium stationary states.

Findings

Derived non-equilibrium fluctuation limits

Characterized stationary fluctuation behavior

Extended fluctuation results to boundary-modified exclusion processes

Abstract

We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha/n$ or $(1-\alpha)/n$ (resp. $\beta/n$ or $(1-\beta)/n$) where $\alpha, \beta>0$ and $n$ is a scaling parameter. We obtain the non-equilibrium fluctuations and consequently the non-equilibrium stationary fluctuations.