Miura Kosuke, Izumida Yuki, Okuda Koji
Department of Physics, Hokkaido University, Sapporo 060-0810, Japan.
Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan.
Phys Rev E. 2021 Apr;103(4-1):042125. doi: 10.1103/PhysRevE.103.042125.
We study the possibility of achieving the Carnot efficiency in a finite-power underdamped Brownian Carnot cycle. Recently, it was reported that the Carnot efficiency is achievable in a general class of finite-power Carnot cycles in the vanishing limit of the relaxation times. Thus, it may be interesting to clarify how the efficiency and power depend on the relaxation times by using a specific model. By evaluating the heat-leakage effect intrinsic in the underdamped dynamics with the instantaneous adiabatic processes, we demonstrate that the compatibility of the Carnot efficiency and finite power is achieved in the vanishing limit of the relaxation times in the small temperature-difference regime. Furthermore, we show that this result is consistent with a trade-off relation between power and efficiency by explicitly deriving the relation of our cycle in terms of the relaxation times.
我们研究了在有限功率欠阻尼布朗卡诺循环中实现卡诺效率的可能性。最近有报道称，在弛豫时间趋于零的极限情况下，卡诺效率在一类一般的有限功率卡诺循环中是可以实现的。因此，通过使用一个具体模型来阐明效率和功率如何依赖于弛豫时间可能会很有趣。通过用瞬时绝热过程评估欠阻尼动力学中固有的热泄漏效应，我们证明了在小温差 regime 中，在弛豫时间趋于零的极限情况下，卡诺效率和有限功率是兼容的。此外，通过明确推导我们的循环在弛豫时间方面的关系，我们表明这个结果与功率和效率之间的权衡关系是一致的。
