Time-reversal symmetric Crooks and Gallavotti–Cohen fluctuation relations in driven classical Markovian systems

In this paper, we address an important question of the relationship between fluctuation theorems for the dissipated work with general finite-time (like Jarzynski equality and Crooks relation) and infinite-time (like Gallavotti–Cohen theorem) drive protocols and their time-reversal symmetric versions. The relations between these kinds of fluctuation relations are uncovered based on the examples of a classical Markovian N-level system. Further consequences of these relations are discussed with respect to the possible experimental verifications. (stochastic thermodynamics)