Geometric Bounds on the Power of Adiabatic Thermal Machines

Abstract

We analyze the performance of slowly driven meso- and micro-scale refrigerators and heat engines that operate between two thermal baths with small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat-leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasi-static limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.

7+6 pages, 2+1 figures

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• Geometric energy transport and refrigeration with driven quantum dots
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines
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• Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings