Current reversal and exclusion processes with history-dependent random walks

TL;DR

This paper introduces a class of exclusion processes with history-dependent random walks, revealing current reversal phenomena due to non-local interactions mediated by particle trails, supported by analytical and simulation results.

Contribution

It presents a novel exclusion process model with history-dependent dynamics and analyzes the resulting current reversal phenomena, combining analytical and simulation approaches.

Findings

Current reversal as a function of particle density.

Non-local interactions cause trail-mediated correlations.

Analytical and simulation results agree on key behaviors.

Abstract

A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate by breaking and reforming lattice bonds. We determine the steady-state current on a ring, and find current-reversal as a function of particle density. This phenomenon is attributed to the non-local interaction between the walkers through their trails, which originates from strong correlations between the dynamics of the particles and the lattice. We rationalize our findings within an effective description in terms of quasi-particles which we call front barriers. Our analytical results are complemented by stochastic simulations.