Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
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DOI：
10.1103/physrevresearch.3.043093
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发表时间：
2021-11-01
影响因子：
4.2
通讯作者：
Ito, Sosuke
中科院分区：
文献类型：
--
作者：
Nakazato, Muka;Ito, Sosuke
我们研究福克普朗克方程的最优输运理论与随机热力学之间的关系。我们表明，熵产生的下限是通过 L-2-Wasserstein 距离的路径长度测量的作用。因为 L-2-Wasserstein 距离是最优传输理论的几何度量，所以我们的结果意味着熵产生的几何解释。基于这种解释，我们获得了转变时间和熵产生之间的热力学权衡关系。这种热力学权衡关系被认为是热力学速度极限，它给出了熵产生的更严格的界限。我们还讨论了子系统的随机热力学，并推导了部分熵产生的下界，作为信息热力学第二定律的推广。我们的形式主义还提供了最佳协议的几何图，以最大限度地减少熵的产生。我们通过最佳随机热机来说明这些结果，并显示效率的几何界限。
We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L-2-Wasserstein distance. Because the L-2-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency.