The optimal efficiency of quantum (or classical) heat engines whose heatbaths are $n$-particle systems is given by the information geometry and thestrong large deviation. We give the optimal work extraction process as aconcrete energy-preserving unitary time evolution among the heat baths and thework storage. We show that our optimal work extraction turns the disorderedenergy of the heat baths to the ordered energy of the work storage, byevaluating the ratio of the entropy difference to the energy difference in theheat baths and the work storage, respectively. By comparing the statisticalmechanical optimal efficiency with the macroscopic thermodynamic bound, weevaluate the accuracy of the macroscopic thermodynamics with finite-size heatbaths from the statistical mechanical viewpoint. We also evaluate the quantumcoherence effect on the optimal efficiency of the cycle processes withoutrestricting their cycle time, by comparing the classical and quantum optimalefficiencies.
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