Effective ergodicity breaking in an exclusion process with varying system length

TL;DR

This paper investigates an exclusion process with variable length, revealing ergodicity breaking phenomena influenced by initial conditions, and draws parallels with a site-dependent random walk, highlighting new physical effects in such stochastic systems.

Contribution

It introduces a variation of the exclusion process with Langmuir kinetics and demonstrates ergodicity breaking, a novel effect in systems with changing length.

Findings

Ergodicity can be broken depending on initial length and parameters.

The process exhibits asymptotic growth behavior influenced by initial conditions.

A related random walk model shows similar ergodic properties.

Abstract

Stochastic processes of interacting particles 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.