A Class of Exclusion Processes Capable of Exhibiting Current Reversal

TL;DR

This paper introduces a class of generalized exclusion processes where the stationary state is governed by the Ising measure, revealing phenomena like current reversal and demonstrating that long-range interactions in dynamics do not necessarily lead to long-range potentials.

Contribution

The work presents a new class of exclusion processes with Ising measure stationary states, showing current reversal and short-range potentials despite long-range interactions, unifying several known models.

Findings

Stationary current can reverse direction in these models.

Long-range dynamic interactions do not imply long-range potentials.

Includes models like ASEP, KLS, and others as special cases.

Abstract

A century after Ising introduced the Ising measure to study equilibrium systems, its relevance has expanded well beyond equilibrium contexts, notably appearing in non-equilibrium frameworks such as the Katz--Lebowitz--Spohn (KLS) model. In this work, we investigate a class of generalized asymmetric simple exclusion processes (ASEP) for which the Ising measure serves as the stationary state. We show that the average stationary current in these models can display current reversal and other unconventional behaviors, offering new insights into transport phenomena in non-equilibrium systems. Moreover, although long-range interaction rates often give rise to long-range interactions in the potential function, our model provides a counterexample: even with long-range interactions in the dynamics, the resulting potential remains short-ranged. Finally, our framework encompasses several well-known models as special cases, including ASEP, the KLS model, the facilitated exclusion process, the cooperative exclusion process, and the assisted exchange model.