Thermodynamic geometry for quantum thermal machines

October 24, 2023, 1:15 p.m. (CEST)

Seminar: Topical Issues of Theoretical Physics

Time: October 24, 2023, 1:15 p.m. (CEST)
Lecturer: Joshua Eglinton (University of Nottingham)
Venue: Universität Stuttgart, Raum 4.331 (NWZ II), Pfaffenwaldring 57, Stuttgart-Vaihingen
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Thermodynamic geometry provides a physically transparent framework to describe non-equilibrium processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. In this approach, figures of merit of thermodynamic cycles can be related to geometric quantities; for instance, the dissipation incurred by a given cycle can be expressed in terms of the length of the control path with respect to a system-dependent metric in the space of control parameters. It thus becomes possible to derive universal trade-off relations between power and efficiency of thermal machines and to explore how quantum effects alter their performance. 

In this talk, I develop the thermodynamic geometry of ideal quantum gases that are coupled to a heat and matter reservoir. As an application of this theory, I will work out a minimal model of a quantum many-body heat engine, whose performance is enhanced by Bose-Einstein condensation as a genuine collective quantum effect. 
In the second part of this talk, I show how thermodynamic geometry can be used to derive a trade-off relation between the coefficient of performance (COP) and the cooling power of microscopic refrigerators. This derivation is based on a general scaling argument and leads to two main results. First, the COP may reach the Carnot bound only if heat-leaks between the cold and the hot reservoir can be fully suppressed. Second, the cooling power of the device close to the Carnot limit is determined by second-order terms in the applied temperature gradient, which are neglected in standard linear-response theory.

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