Effective ergodicity breaking in an exclusion process with varying system length
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 onedimensional 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 sitedependent hopping probabilities exhibits qualitatively the same behavior.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 September 2015
 DOI:
 10.1016/j.physa.2015.03.068
 arXiv:
 arXiv:1409.0329
 Bibcode:
 2015PhyA..433..100S
 Keywords:

 Nonequilibrium physics;
 Stochastic process;
 Queueing theory;
 Exclusion process;
 Langmuir kinetics;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Biological Physics;
 Quantitative Biology  Quantitative Methods
 EPrint:
 5 pages, 7 figures