Department of Physics No. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev E. 2018 Jun;97(6-1):062101. doi: 10.1103/PhysRevE.97.062101.
We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency-Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet-can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the second law. Finally, we discuss the connection between heat and entropy in a nonthermal situation where the friction and noise intensity are state dependent.
我们根据系统及其环境中的总熵产生，推导出朗之万系统广义电流的界。对于过阻尼动力学，任何广义电流都受到总熵产生速率的限制。我们表明，广义电流幅度的这种熵界对与热浴接触的棘轮施加了功率-效率权衡关系：最大效率-卡诺效率（对于斯莫卢科夫斯基-费曼棘轮）和单位效率（对于闪烁或摇摆棘轮）只能在功率输出为零时达到。对于欠阻尼动力学，虽然可能存在不受熵产生速率限制的可逆电流，但我们表明输出功率和热吸收速率是不可逆电流，因此服从相同的界。因此，功率-效率权衡关系不仅适用于欠阻尼棘轮，也适用于周期性驱动的热机。对于弱驱动，该界在由第二定律施加的限制之外，对昂萨格矩阵产生了额外的约束。最后，我们讨论了在摩擦和噪声强度与状态相关的非热情况下，热量和熵之间的联系。
