Quantum thermal absorption machines: refrigerators, engines and clocks

Abstract

The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introduction to the physics of quantum absorption machines, covering refrigerators, engines and clocks in detail.

Keywords:

• Quantum thermodynamics
• open quantum systems

Acknowledgments

Useful discussions with John Goold during the preparation of the manuscript are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Mark T. Mitchison http://orcid.org//0000-0003-3805-3880

Notes

1 Complete positivity means that the operation $\mathcal{E}\otimes \mathcal{I}$ is positive, where $\mathcal{I}$ is the identity superoperator acting on an arbitrary auxiliary system.

2 Strictly speaking, there could be multiple jump operators ${\hat{A}}_j\left(\omega \right)$ and rates ${\gamma }_j\left(\omega \right)$ for each transition frequency ω, but we do not need to consider such complications here.

3 Some treatments use the alternative designation $T_h$ for the hottest reservoir and $T_r$ for the intermediate (‘room-temperature’) reservoir.

4 Indeed, equilibrium states span the set of completely passive states, i.e. those which remain passive under composition, such that ${\rho }^{\otimes n}$ is passive for all n [91–93].

Additional information

Funding

This work was funded by the European Research Council research and innovation program (grant agreement 758403).

Notes on contributors

Mark T. Mitchison

Mark Mitchison is a theoretical physicist based at Trinity College Dublin. Mark wrote his PhD thesis on atomic-scale absorption refrigerators and thermometers at Imperial College London in 2016. He then worked for two years at Universität Ulm before moving to Dublin in 2018. His research focuses on open quantum systems and their applications as thermal machines and as platforms for investigating non-equilibrium physics.