Optimal Efficiency of Heat Engines with Finite-Size Heat Baths

TL;DR

This paper investigates the maximum efficiency of quantum and classical heat engines with finite-size heat baths, using information geometry and large deviation theory, and compares microscopic and macroscopic efficiency bounds.

Contribution

It provides a concrete energy-preserving process for optimal work extraction and analyzes quantum coherence effects on efficiency without cycle time restrictions.

Findings

Optimal work extraction process derived as a unitary evolution.

Quantum coherence can enhance efficiency compared to classical limits.

Finite-size effects cause deviations from macroscopic thermodynamic bounds.

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 mechanical optimal efficiency with the macroscopic thermodynamic bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint. We also evaluate the quantum coherence effect on the optimal efficiency of the cycle processes without restricting their cycle time, by comparing the classical and quantum optimal efficiencies.