On the range of validity of the fluctuation theorem for stochastic Markovian dynamics

TL;DR

This paper investigates the conditions under which the Gallavotti-Cohen symmetry holds for current fluctuations in stochastic Markovian systems, revealing its breakdown in infinite state spaces like the Zero-Range Process and extending analytical results to multiple sites.

Contribution

It provides a detailed analysis of the validity of the fluctuation theorem in systems with infinite state spaces and extends previous results to multi-site models.

Findings

Gallavotti-Cohen symmetry holds in finite state systems.

Symmetry breaks down in infinite state systems like ZRP.

Numerical methods may fail in certain phases due to spectral gaps.

Abstract

We consider the fluctuations of generalized currents in stochastic Markovian dynamics. The large deviations of current fluctuations are shown to obey a Gallavotti-Cohen (GC) type symmetry in systems with a finite state space. However, this symmetry is not guaranteed to hold in systems with an infinite state space. A simple example of such a case is the Zero-Range Process (ZRP). Here we discuss in more detail the already reported breakdown of the GC symmetry in the context of the ZRP with open boundaries and we give a physical interpretation of the phases that appear. Furthermore, the earlier analytical results for the single-site case are extended to cover multiple-site systems. We also use our exact results to test an efficient numerical algorithm of Giardina, Kurchan and Peliti, which was developed to measure the current large deviation function directly. We find that this method breaks down in some phases which we associate with the gapless spectrum of an effective Hamiltonian.