Dynamics of non-Markovian exclusion processes

TL;DR

This paper develops a framework to analyze how non-Markovian noise influences the behavior of exclusion processes, revealing the impact of memory effects on particle current-density relations in driven diffusive systems.

Contribution

It introduces a general method to derive the fundamental diagram of ASEPs with non-Poissonian noise using mean residual lifetime and correlation length.

Findings

Memory effects alter current-density relations in exclusion processes.

The framework accurately predicts system behavior under various non-Poissonian noise statistics.

Numerical simulations support the theoretical predictions.

Abstract

Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.