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

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.