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There are two related theorems which hold even in far from equilibrium,namely fluctuation theorem and Jarzynski equality. Fluctuation theorem statesthe existence of symmetry of fluctuation of entropy production, while Jarzynskiequality enables us to estimate the free energy change between two states byusing irreversible processes. On the other hand, relationship between thesetheorems was investigated by Crooks for the classical stochastic systems. Inthis letter, we derive quantum analogues of fluctuation theorem and Jarzynskiequality microscopic reversibility condition. In other words, the quantumanalogue of the work by Crooks is presented.Comment: 7pages, revised versio

Unified treatment of the quantum fluctuation theorem and the Jarzynski equality in terms of microscopic reversibility