A Gallavotti-Cohen-Evans-Morriss like symmetry for a class of Markov jump processes

TL;DR

This paper uncovers a new symmetry in the large deviation functions of certain time-integrated currents in specific Markov jump processes, extending the understanding of fluctuation symmetries beyond entropy production.

Contribution

It introduces a novel symmetry similar to Gallavotti-Cohen, applicable to a restricted class of Markov jump processes with particular transition structures and constraints.

Findings

Identifies a new symmetry in large deviation functions

Provides three physical examples demonstrating the symmetry

Links the symmetry to time-reversal through trajectory grouping

Abstract

We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochatic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.