论文标题
动力学模型的Bellman方程和最佳本地翻转策略
The Bellman equation and optimal local flipping strategies for kinetic Ising models
论文作者
论文摘要
热力学，信息和工作提取之间有着深厚的联系。自热力学诞生以来，已经引入了各种类型的麦克斯韦恶魔，以加深我们对第二定律的理解。多亏了他们，人们已经表明，热力学和信息之间以及在热系统中的信息和工作之间存在着深厚的联系。在本文中，我们研究了从热力学系统中提取能量的问题，从而满足了具有完美信息的代理，例如在ISING模型的背景下，它具有由Bellman方程解决方案给出的最佳策略。与麦克斯韦的魔鬼相比，我们称这些代理商称为kobolds，而麦克斯韦的恶魔不一定需要满足详细的平衡。这与典型的蒙特卡洛算法形成鲜明对比，后者在每个时间步骤中随机选择动作。因此，将这些kobolds的行为与大都市算法进行比较是很自然的。对于各种Ising模型，我们在数值和分析上研究最佳策略的特性，表明Kobold的行为是表征其策略的参数的函数。
There is a deep connection between thermodynamics, information and work extraction. Ever since the birth of thermodynamics, various types of Maxwell demons have been introduced in order to deepen our understanding of the second law. Thanks to them it has been shown that there is a deep connection between thermodynamics and information, and between information and work in a thermal system. In this paper, we study the problem of energy extraction from a thermodynamic system satisfying detailed balance, from an agent with perfect information, e.g. that has an optimal strategy, given by the solution of the Bellman equation, in the context of Ising models. We call these agents kobolds, in contrast to Maxwell's demons which do not necessarily need to satisfy detailed balance. This is in stark contrast with typical Monte Carlo algorithms, which choose an action at random at each time step. It is thus natural to compare the behavior of these kobolds to a Metropolis algorithm. For various Ising models, we study numerically and analytically the properties of the optimal strategies, showing that there is a transition in the behavior of the kobold as a function of the parameter characterizing its strategy.
