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

TL;DR

This paper develops a thermodynamic geometric framework for ideal quantum gases, applying it to quantum heat engines with Bose gases, revealing how quantum many-body effects can enhance power output compared to single-particle engines.

Contribution

It extends thermodynamic geometry to driven quantum gases and models a Bose gas engine, linking quantum effects to power enhancement in thermal machines.

Findings

Bose-gas engine delivers more power at fixed efficiency than single-body engines.

The geometric framework captures BEC-induced power enhancement.

Quantum many-body effects significantly impact thermal machine performance.

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 BEC-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model [New J. Phys. 24, 025001 (2022)]. 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.