Splitting rate matrix as a definition of time reversal in master equation systems

TL;DR

This paper introduces a new way to define time reversal in stochastic master equations by splitting the rate matrix, enabling the derivation of various fluctuation relations and revising entropy production formulas.

Contribution

It proposes a novel matrix splitting approach to define time reversal, linking fluctuation relations and modifying entropy production in master equation systems.

Findings

Fluctuation relations depend on the matrix splitting.

Entropy production formulas need modification with reversible parts.

The approach unifies different fluctuation relations.

Abstract

Motivated by recent progresses in nonequilibrium Fluctuation Relations, we present a generalized time reversal for stochastic master equation systems with discrete states that is defined as a splitting of the rate matrix into irreversible and reversible parts. An immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splitting. Additionally, we also find that, the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the presence of the reversible part, which was completely ignored in the past a long time.