Quantum heat engines with complex working media, complete Otto cycles and heuristics

TL;DR

This paper investigates the efficiency and performance of quantum Otto engines with complex spin systems, deriving conditions and heuristics that connect engine performance to quantum interactions and majorization theory.

Contribution

It extends the analysis of quantum Otto engines to arbitrary spin magnitudes and formulates heuristics for engine performance based on extreme-case scenarios.

Findings

Efficiency bounds depend on spin interactions and magnitudes.

Heuristics relate engine performance to majorization principles.

Complete Otto cycle analysis reveals average performance insights.

Abstract

Quantum thermal machines make use of non-classical thermodynamic resources, one of which is interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been earlier shown that the said interaction provides an enhancement of cycle efficiency for two spin-1/2 particles, with an upper bound which is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. Analyzing extreme-case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spins model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Further, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.