An integral fluctuation theorem for systems with unidirectional transitions

TL;DR

This paper derives an integral fluctuation theorem for Markovian jump processes with unidirectional transitions, revealing new insights into entropy production and residence times in such non-reversible systems.

Contribution

It introduces an integral fluctuation theorem applicable to systems with unidirectional transitions, extending fluctuation relations beyond microreversible dynamics.

Findings

The fluctuation theorem holds for systems with unidirectional transitions.

Numerical analysis shows similar convergence properties as reversible systems.

The theorem involves entropy and residence time contributions.

Abstract

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where $R_{ij} >0$ but $R_{ji} =0$, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically, and found to show the same qualitative features as in systems exhibiting microreversibility.