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Open AccessArticle

Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

1
Dipartimento Scienza Applicata e Tecnologia, 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), Via dei Taurini 19, 00185 Roma, Italy
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1028; https://doi.org/10.3390/e21111028
Received: 30 September 2019 / Revised: 18 October 2019 / Accepted: 20 October 2019 / Published: 23 October 2019
(This article belongs to the Special Issue The Ubiquity of Entropy)
Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model. View Full-Text
Keywords: driven diffusive systems; totally asymmetric simple exclusion process; dynamical transition driven diffusive systems; totally asymmetric simple exclusion process; dynamical transition
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Pelizzola, A.; Pretti, M.; Puccioni, F. Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model. Entropy 2019, 21, 1028.

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