Measurement-based Formulation of Quantum Heat Engine and Optimal Efficiency with Finite-Size Effect

Hiroyasu Tajima, Masahito Hayashi

Published Apr 23, 2015• 0 citations

Abstract

There exist two formulations for quantum heat engine. One is semi-classical scenario, and the other is full quantum scenario. The former is formulated as a unitary evolution for the internal system (working body and heat baths), and is adopted by the community of statistical mechanics. The latter is formulated as a unitary for the work storage and the internal system. It is adopted by the community of quantum information. However, these formulations do not consider measurement process. In this paper, we formulate the quantum heat engine based on the quantum measurement theory, because the amount of extracted work should be observed in a practical situation. With using our formulation, we derive two trade-off relations that show the semi-classical scenario does not work when the amount of extracted work is observed, i.e., we can hardly know the amount of the extracted work when the time evolution of the internal system is close to unitary. Next, based on our formulation, we derive the optimal efficiency of quantum heat engines with the finite-size heat baths, without assuming the existence of quasi-static processes. Using the strong large deviation theory, we asymptotically expand the optimal efficiency up to the third order. The first term is shown to be Carnot efficiency, and the higher order terms are shown to be the finite-size effects of the heat baths. We can construct the optimal work extraction as an energy-preserving unitary evolution among the internal system and the work storage. During the optimal work extraction, the entropy gain of the work storage is so negligibly small as compared with the energy gain of the work storage.

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