Realm of Validity of the Crooks Relation
arXiv:1012.5308 · doi:10.1103/PhysRevE.83.041129
Abstract
We consider the distribution $P(Ï)$ of the Hatano-Sasa entropy, $Ï$, in reversible and irreversible processes, finding that the Crooks relation for the ratio of the pdf's of the forward and backward processes, $P_F(Ï)/P_R(-Ï)=e^Ï$, 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 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 Crooks relation despite their irreversibility and violation of detailed balance. We verify these results in selected cases numerically.
6 figures, version to appear in Physical Review E