Measurement-based formulation of quantum heat engines

Abstract

There exist two formulations for quantum heat engines that model energy transfer between two microscopic systems. One is the semiclassical scenario and the other is the full quantum scenario. The former is formulated as unitary evolution for the internal system and is adopted by the statistical mechanics community. In the latter, the whole process is formulated as unitary and is adopted by the quantum information community. This paper proposes a model for quantum heat engines that transfer energy from a collection of microscopic systems to a macroscopic system like a fuel cell. In such a situation, the amount of extracted work is visible for a human. For this purpose, we formulate a quantum heat engine as the measurement process whose measurement outcome is the amount of extracted work. Under this model, we derive a suitable energy-conservation law and propose a more concrete submodel. Then we derive a trade-off relation between the measurability of the amount of work extraction and the coherence of the internal system, which limits the applicability of the semiclassical scenario to a heat engine transferring energy from a collection of microscopic systems to a macroscopic system.