Spins-based Quantum Otto Engines and Majorisation

TL;DR

This paper uses majorisation theory to analyze the performance and efficiency of quantum Otto engines with spin systems, providing conditions for work extraction and thermodynamic bounds.

Contribution

It introduces majorisation as a criterion for quantum Otto engine operation and derives new conditions for work extraction in spin systems.

Findings

Majorisation provides necessary and sufficient conditions for engine operation.

Derived criteria for positive work extraction in spin-1/2 systems with Heisenberg interaction.

Established an upper bound on quantum Otto engine efficiency using majorisation.

Abstract

The concept of majorisation is explored as a tool to characterize the performance of a quantum Otto engine in the quasi-static regime. For a working substance in the form of a spin of arbitrary magnitude, majorisation yields a necessary and sufficient condition for the operation of the Otto engine, provided the canonical distribution of the working medium at the hot reservoir is majorised by its canonical distribution at the cold reservoir. For the case of a spin-1/2 interacting with an arbitrary spin via isotropic Heisenberg exchange interaction, we derive sufficient criteria for positive work extraction using the majorisation relation. Finally, local thermodynamics of spins as well as an upper bound on the quantum Otto efficiency is analyzed using the majorisation relation.