On the symmetry of current probability distributions in jump processes

TL;DR

This paper investigates the conditions under which non-entropic currents in Markov jump processes exhibit symmetric large deviation functions, revealing new symmetries related to cycle degeneracies and time-reversal.

Contribution

It provides a necessary condition for symmetry in non-entropic currents and demonstrates explicit examples in 4-state systems, expanding understanding of fluctuation symmetries.

Findings

Symmetry in non-entropic currents linked to cycle degeneracies.

Explicit examples of symmetric non-entropic currents in 4-state systems.

Symmetries are related to time-reversal when trajectories are grouped appropriately.

Abstract

We study the symmetry of large deviation functions associated with time-integrated currents in Markov pure jump processes. One current known to have this symmetry is the fluctuating entropy production and this is the content of the fluctuation theorem. Here we obtain a necessary condition in order to have a current different from entropy with a symmetric large deviation function. This condition is related to degeneracies in the set of increments associated with fundamental cycles from Schnakenberg network theory. Moreover we consider 4-states systems where we explicitly show that non-entropic time-integrated currents can be symmetric. We also show that these new symmetries, as is the case of the fluctuation theorem, are related to time-reversal. However, this becomes apparent only when stochastic trajectories are appropriately grouped together.