Abstract
We consider the distribution P(Φ) of the Hatano-Sasa entropy, Φ, in reversible and irreversible processes, finding that the Crooks relation for the ratio of the probability density functions of the forward and backward processes, P(F)(Φ)/P(R)(-Φ)=e(Φ), is satisfied not only for reversible, but also for irreversible processes, in general, in the adiabatic limit of "slow processes." Focusing on systems with a finite set of discrete states (and no absorbing states), we observe that two-state systems always fulfill detailed balance, and obey the Crooks relation. We also identify a wide class of systems, with more than two states, that can be "coarse grained" into two-state systems and obey the Crooks relation despite their irreversibility and violation of detailed balance. We verify these results in selected cases numerically.
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