Eglinton Joshua, Brandner Kay
School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Phys Rev E. 2022 May;105(5):L052102. doi: 10.1103/PhysRevE.105.L052102.
We analyze the performance of slowly driven meso- and microscale refrigerators and heat engines that operate between two thermal baths with a 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 quasistatic 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.
我们分析了在两个温差较小的热库之间运行的缓慢驱动的介观和微观尺度冰箱及热机的性能。通过一般的标度论证，我们表明，只有当热库之间的热泄漏被完全抑制时，此类装置才能任意接近其卡诺极限运行。此时它们的功率输出受到一个通用的几何界限限制，该界限在卡诺极限处呈二次方衰减至零。如果驱动协议经过适当优化且热库之间的温差随驱动频率趋于零，那么在准静态极限下这个界限可以渐近饱和。这些结果在任何具有明确绝热响应区域和广义昂萨格对称性的热力学一致动力学的一般条件下都成立。为作说明，我们给出了一个作为冷却装置运行的量子比特冰箱和一个相干电荷泵的模型。
