Non equilibrium stationary state for the SEP with births and deaths

TL;DR

This paper investigates the stationary density profile of the symmetric simple exclusion process with boundary births and deaths in a large interval, extending previous models to analyze non-equilibrium stationary states.

Contribution

It provides a detailed analysis of the stationary measure density profile for the SEP with boundary-driven births and deaths in the large system limit.

Findings

Characterization of the stationary density profile in the large N limit

Extension of boundary conditions to include births and deaths

Insights into non-equilibrium stationary states for exclusion processes

Abstract

We consider the symmetric simple exclusion process in the interval $\La_N:=[-N,N]\cap\mathbb Z$ with births and deaths taking place respectively on suitable boundary intervals $I_+$ and $I_-$, as introduced in De Masi et al. (J. Stat. Phys. 2011). We study the stationary measure density profile in the limit $N\to\infty$