Dynamic and static large deviations of a one dimensional SSEP in weak contact with reservoirs

TL;DR

This paper derives a formula for the quasi-potential of a one-dimensional symmetric exclusion process with weak boundary contact, revealing how boundary interactions influence large deviations and the evolution of the system over different time scales.

Contribution

It provides a new explicit formula for the quasi-potential of the SSEP with weak reservoirs, connecting boundary interaction strength to large deviation behavior.

Findings

The density profile behaves as with reflecting boundaries in the diffusive scale.

Total mass evolution requires a longer time-scale observation.

The boundary interaction is so weak that it affects the system only in extended time scales.

Abstract

We derive a formula for the quasi-potential of one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of the exclusion process with reflecting boundary conditions. In order to observe an evolution of the total mass, the process has to be observed in a longer time-scale, in which the density profile becomes immediately constant.