Kheradsoud Sara, Dashti Nastaran, Misiorny Maciej, Potts Patrick P, Splettstoesser Janine, Samuelsson Peter
Physics Department and NanoLund, Lund University, S-221 00 Lund, Sweden.
Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden.
Entropy (Basel). 2019 Aug 8;21(8):777. doi: 10.3390/e21080777.
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.
在热机运行中，大功率输出、高效率与小波动之间的权衡，近来在热力学不确定性关系（TURs）的背景下受到了关注。在此，我们通过理论研究具有能量依赖传输函数的量子点接触（QPC）作为稳态热电热机的运行情况，给出了这种权衡的具体示例。作为起点，我们回顾并扩展了先前关于功率产生和效率的分析。此后，将功率波动以及TURs对功率、效率和波动共同施加的限制作为额外的性能量化指标进行分析。我们考虑QPC传输概率具有任意平滑性，其在能量上呈现出接近阶跃状的依赖关系，并同时考虑线性和非线性运行 regime。结果发现，在广泛的参数范围内，功率产生接近其理论最大值，效率超过卡诺效率的一半，并且波动相当小。此外，我们表明，通过要求非零功率产生，在线性 regime中，可以根据热电品质因数制定更强的TUR。有趣的是，对于我们的QPC器件，这个限制在超出线性响应的广泛参数 regime中也成立。
