Quantum Thermodynamics of a Power-Law Potential

TL;DR

This paper models quantum thermal machines using power-law potentials, deriving energy spectra and efficiency expressions to optimize performance and understand operation modes in quantum heat engines.

Contribution

It introduces a comprehensive analysis of quantum heat engines with power-law potentials, deriving key thermodynamic quantities and identifying parameters for optimized performance.

Findings

Energy spectra recover harmonic oscillator and 1-D potential well forms

Expressions for energy exchanges and efficiency as functions of parameters

Identification of parameters for optimized engine performance

Abstract

Modeling quantum thermal machines provides a practical approach to describing the thermodynamic properties of quantum technologies and devices. For this purpose, power-law potentials are often employed as working mediums of quantum thermodynamic cycles to investigate the concepts of heat, work, and efficiency. With this in mind, we present the results for the Stirling and Otto numerical modeling of quantum thermal machines that use a general power law potential with a characteristic $q$ exponent. We calculate its energy spectra, showing that it recovers the traditional forms of harmonic oscillator and 1-D potential well. We derive expressions for the reduced energy exchanges during a complete cycle and for the efficiency/coefficient of performance as a function of the exponent $q$, the bath temperatures, and the frequency ratio. From these results, we identify parameters that yield desired properties, such as optimized performance and transitions between different operation modes. The findings highlight the role of power-like potentials in optimizing quantum heat engines and support the design of tailored engines with specific performance characteristics.