Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics

TL;DR

This paper investigates the breakdown of Gallavotti-Cohen symmetry in current fluctuations within a stochastic zero-range process, highlighting how unbounded state spaces can lead to such deviations and exploring initial state effects.

Contribution

It demonstrates that large current fluctuations can violate Gallavotti-Cohen symmetry in systems with unbounded state spaces, a novel insight into fluctuation theorems.

Findings

Large current fluctuations do not satisfy Gallavotti-Cohen symmetry.

Breakdown of symmetry is linked to unbounded state spaces.

Initial conditions influence the asymptotic current distribution.

Abstract

We consider the behaviour of current fluctuations in the one-dimensional partially asymmetric zero-range process with open boundaries. Significantly, we find that the distribution of large current fluctuations does not satisfy the Gallavotti-Cohen symmetry and that such a breakdown can generally occur in systems with unbounded state space. We also discuss the dependence of the asymptotic current distribution on the initial state of the system.