Optimal Efficiency of Heat Engines with Finite-Size Heat Baths

Abstract

The optimal efficiency of quantum (or classical) heat engines whose heat baths are \(n\)-particle systems is given by the information geometry and the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistical machanical optimal efficiency with the macroscopic thermodynamical bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint.