Exact solution of a heterogeneous multi-lane asymmetric simple exclusion process

TL;DR

This paper presents an exact, factorized solution for a heterogeneous multi-lane TASEP with lane-changing rates, revealing that particle current depends solely on lane-changing parameters, not lane configuration.

Contribution

It introduces an exact, separable solution for a multi-lane TASEP with heterogeneity, under detailed balance conditions, and derives a simple expression for particle current.

Findings

Particle current depends only on lane-changing parameters.

The solution is factorized and separable due to detailed balance.

Analytical expression for current in the thermodynamic limit.

Abstract

We prove an exact solution of a multi-lane totally asymmetric simple exclusion process (TASEP) with heterogeneous lane-changing rates on a torus. The solution is given by a factorized form; that is, the TASEP in each lane and lane-changing transition can be separable because of the detailed balance conditions in lane-changing transition. Using the saddle point method, the current of particles is calculated in a simple form in a thermodynamic limit. It is notable that the current depends only on a set of lane-changing parameters, not on the configuration of lanes.