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Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine

1
Physics Department and NanoLund, Lund University, S-221 00 Lund, Sweden
2
Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 777; https://doi.org/10.3390/e21080777
Received: 11 May 2019 / Revised: 3 July 2019 / Accepted: 29 July 2019 / Published: 8 August 2019
(This article belongs to the Special Issue Quantum Transport in Mesoscopic Systems)
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Abstract

The trade-off between large power output, high efficiency and small fluctuations in the operation of heat engines has recently received interest in the context of thermodynamic uncertainty relations (TURs). Here we provide a concrete illustration of this trade-off by theoretically investigating the operation of a quantum point contact (QPC) with an energy-dependent transmission function as a steady-state thermoelectric heat engine. As a starting point, we review and extend previous analysis of the power production and efficiency. Thereafter the power fluctuations and the bound jointly imposed on the power, efficiency, and fluctuations by the TURs are analyzed as additional performance quantifiers. We allow for arbitrary smoothness of the transmission probability of the QPC, which exhibits a close to step-like dependence in energy, and consider both the linear and the non-linear regime of operation. It is found that for a broad range of parameters, the power production reaches nearly its theoretical maximum value, with efficiencies more than half of the Carnot efficiency and at the same time with rather small fluctuations. Moreover, we show that by demanding a non-zero power production, in the linear regime a stronger TUR can be formulated in terms of the thermoelectric figure of merit. Interestingly, this bound holds also in a wide parameter regime beyond linear response for our QPC device. View Full-Text
Keywords: thermoelectricity; heat engines; quantum transport; mesoscopic physics; fluctuations; thermodynamic uncertainty relations thermoelectricity; heat engines; quantum transport; mesoscopic physics; fluctuations; thermodynamic uncertainty relations
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Kheradsoud, S.; Dashti, N.; Misiorny, M.; Potts, P.P.; Splettstoesser, J.; Samuelsson, P. Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine. Entropy 2019, 21, 777.

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