Simple Exclusion Processes with Local Resetting

TL;DR

This paper studies how local resetting affects the stationary states of symmetric and asymmetric simple exclusion processes on a ring, revealing complex phase behavior and regimes depending on resetting rate scaling.

Contribution

It introduces and analyzes simple exclusion processes with local resetting, uncovering multiple phases and regimes, especially in the asymmetric case, using mean-field and simulation methods.

Findings

Identification of three regimes in the thermodynamic limit

Discovery of four phases in the asymmetric model with intermediate resetting

Observation of phase separation and rich behavior depending on resetting rate scaling

Abstract

We investigate the stationary state of Symmetric and Totally Asymmetric Simple Exclusion Processes with local resetting, on a one-dimensional lattice with periodic boundary conditions, using mean-field approximations, which appear to be exact in the thermodynamic limit, and kinetic Monte Carlo simulations. In both cases we find that in the thermodynamic limit the models exhibit three different regimes, depending on how the resetting rate scales with the system size. The Totally Asymmetric version of the model has a particularly rich behaviour, especially in an intermediate resetting regime where the resetting rate vanishes as the inverse of the system size, exhibiting 4 different phases, including phase separation.