Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling

TL;DR

This paper develops a general theory for the optimal performance of quantum heat engines with multiple conserved quantities, considering finite-size baths with volume scaling, and demonstrates how physical parameters like particle mass influence engine efficiency.

Contribution

It introduces a fine-grained generalized Carnot bound for finite-size baths with volume scaling and provides a protocol to achieve this bound in quantum thermodynamics.

Findings

Derived a performance bound considering finite-size effects and volume scaling.

Constructed a protocol to attain the optimal engine performance.

Showed particle mass affects efficiency in a gas-based heat engine.

Abstract

In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-i.i.d.~scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.