Eur. Phys. J. B (2017) 90: 183
https://doi.org/10.1140/epjb/e2017-80248-7

Regular Article

Cluster approximations for the TASEP: stationary state and dynamical transition

¹ Dipartimento di Scienza Applicata e Tecnologia and CNISM, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
² INFN, Sezione di Torino, via Pietro Giuria 1, 10125 Torino, Italy
³ Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi (CNR-ISC), 00185 Roma, Italy

^a e-mail: alessandro.pelizzola@polito.it

Received: 28 April 2017
Received in final form: 19 July 2017
Published online: 9 October 2017

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.