Non-Equilibrium Entropy and Irreversibility in Generalized Stochastic Loewner Evolution from an Information-Theoretic Perspective.
Non-Equilibrium Entropy and Irreversibility in Generalized Stochastic Loewner Evolution from an Information-Theoretic Perspective.
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DOI：
10.3390/e23091098
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发表时间：
2021-08-24
期刊：
影响因子：
--
通讯作者：
Saito M
中科院分区：
文献类型：
--
作者：
Shibasaki Y;Saito M
在这项研究中，我们从理论上研究了广义随机Loewner演化（SLE）驱动的可逆朗之万动力学的背景下，非平衡统计力学。利用Loewner进化的能力，这使得编码的非平衡系统到平衡系统，我们制定了编码机制的SLE吉布斯熵为基础的信息理论方法，讨论其优势，作为一种手段，更好地描述非平衡系统。在推导了广义SLE曲线的二维轨迹的熵产生和通量后，我们用Kullback-Leibler（KL）散度重新表述了系统的熵性质。我们表明，这种操作导致的Jarzynski等式和热力学第二定律，这是与先前提出的信息热力学理论相一致的替代表达式。通过将熵分解为可加性和非可加性部分，类似地讨论了2D轨迹的不可逆性。我们数值验证了我们的模型的非平衡性质，通过模拟我们的配方，被称为相对Loewner熵的熵措施的长时间行为。
In this study, we theoretically investigated a generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics in the context of non-equilibrium statistical mechanics. Using the ability of Loewner evolution, which enables encoding of non-equilibrium systems into equilibrium systems, we formulated the encoding mechanism of the SLE by Gibbs entropy-based information-theoretic approaches to discuss its advantages as a means to better describe non-equilibrium systems. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curves, we reformulated the system’s entropic properties in terms of the Kullback–Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectories is similarly discussed by decomposing the entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.
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