Cluster approximations for the TASEP: stationary state and dynamical transition

TL;DR

This paper develops cluster approximation methods for the TASEP, improving on mean-field models by incorporating local correlations, and analyzes the dynamical transition affecting the system's relaxation spectrum.

Contribution

It introduces and tests pair and triplet cluster approximations for TASEP, enhancing understanding of steady states and dynamical transitions beyond mean-field approaches.

Findings

Cluster approximations improve steady state predictions.

Analysis of the dynamical transition spectrum.

Enhanced understanding of local correlations in TASEP.

Abstract

We develop and test cluster approximations, which generalize simple mean--field by taking into account more and more local correlations, for the Totally Asymmetric Simple Exclusion Process with open boundaries. We consider in detail the pair and triplet approximations, discussing the improvements with respect to mean field in various steady state properties. Moreover, we analyze the recently discovered dynamical transition, describing how the spectrum of the relaxation matrix changes at the transition.