Balance network of asymmetric simple exclusion process

TL;DR

This paper analyzes a network of ASEPs with bidirectional links, providing exact steady-state distributions and demonstrating that nonequilibrium systems can be described within an equilibrium statistical mechanics framework.

Contribution

It introduces a general framework for describing balance networks of ASEPs, including special cases like Langmuir kinetics and multiple lanes, with exact steady-state solutions.

Findings

Exact steady-state distributions are derived for the network.

The system's nonequilibrium behavior is captured using equilibrium statistical mechanics.

The approach applies broadly regardless of network structure.

Abstract

We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the ASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, the expressions are well described in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems.