  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.

Statistical Mechanics;Soft Condensed Matter