Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Eglinton, Joshua; Pyhäranta, Tuomas; Saito, Keiji; Brandner, Kay

Abstract

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the Bose-Einstein condensate-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model (Myers et al 2022 New J. Phys. 24 025001). Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

Citation

Eglinton, J., Pyhäranta, T., Saito, K., & Brandner, K. (2023). Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines. New Journal of Physics, 25(4), Article 043014. https://doi.org/10.1088/1367-2630/acc966

• Journal Article Type: Article
• Acceptance Date: Mar 31, 2023
• Online Publication Date: Apr 13, 2023
• Publication Date: Apr 13, 2023
• Deposit Date: May 1, 2023
• Publicly Available Date: May 2, 2023
• Journal: New Journal of Physics
• Electronic ISSN: 1367-2630
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 4
• Article Number: 043014
• DOI: https://doi.org/10.1088/1367-2630/acc966
• Keywords: Thermodynamic geometry, quantum heat engines, quantum thermodynamics, Bose–Einstein condensate
• Public URL: https://nottingham-repository.worktribe.com/output/19454146
• Publisher URL: https://iopscience.iop.org/article/10.1088/1367-2630/acc966
• Additional Information: Article Title: Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines; Journal Title: New Journal of Physics; Article Type: paper; Copyright Information: © 2023 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft; Date Received: 2023-01-05; Date Accepted: 2023-03-31; Online publication date: 2023-04-13