Effective ergodicity breaking in an exclusion process with varying system length

Christoph Schultens, Andreas Schadschneider and Chikashi Arita

Physica A: Statistical Mechanics and its Applications, 2015, vol. 433, issue C, 100-106

Abstract: Stochastic processes of interacting particles in systems with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.

Keywords: Nonequilibrium physics; Stochastic process; Queueing theory; Exclusion process; Langmuir kinetics (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:433:y:2015:i:c:p:100-106

DOI: 10.1016/j.physa.2015.03.068

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