Relations between 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 $W_{d} = W-\Delta F$ with general finite-time (like Jarzynski equality and Crooks relation) and infinite-time (like Gallavotti-Cohen theorem) drive protocols. The relations between these kinds of fluctuation relations are uncovered based on the examples of a classical Markovian $N$-level system. The further consequences of these relations are discussed with respect to the possible experimental verifications.