发表机构
Santa Fe Institute; Complexity Science Hub, Vienna, Austria; Arizona State University; International Centre for Theoretical Physics, Trieste, Italy（圣塔菲研究所; 维也纳复杂性科学中心; 亚利桑那州立大学; 的里雅斯特国际理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对任意物理过程，研究如何设计初始分布（先验）以最小化最坏情况下的熵产生，给出了确定性映射的闭式解，并揭示了随机映射下极小极大先验与玻尔兹曼-吉布斯方程的联系及其失配成本的通用标度行为。
AI 中文摘要
对于任何物理过程，改变其状态上的初始分布将改变由此产生的期望熵产生（EP）。使特定过程的熵产生最小化的初始分布被称为该过程的先验。改变过程的微观物理细节将改变其熵产生。我们考虑以下问题：如果工程师想要设计一个系统来实现给定的映射，那么他们应该在系统中设计什么样的先验，以在最坏情况下的实际分布下最小化熵产生？当映射是确定性的时，我们推导出该问题的闭式解。我们还表明，对于随机映射，最坏情况下的实际分布总是可以被选择为单个状态上的点质量，并且相关的极小极大先验类似于玻尔兹曼-吉布斯方程，并且可以通过全局收敛的数值算法找到。我们还表明，相关的极小极大失配成本是观察输出后剩余的关于输入的最大不确定性。最后，我们将分析扩展到连续时间域，表明极小极大瞬时失配成本发散，而相应的有限时间极小极大失配成本具有由动力学最大逃逸率设定的通用短时间标度。
英文摘要
For any physical process, varying the initial distribution over its states will change the resulting expected entropy production (EP). An initial distribution that minimizes the EP of a particular process is called the prior of that process. Varying the microphysical details of the process will change its prior. We consider the following question: if an engineer wants to design a system to implement a given map, what prior should they design into the system to minimize the EP for the worst-case actual distribution? We refer to the resulting optimal worst-case value as the minimax EP, and investigate how it depends only on the dynamics of the process. We derive the closed-form solution to this minimax problem when the map is deterministic. We also show that for stochastic maps, a worst-case actual distribution can always be chosen to be a point mass on a single state, and that the associated minimax prior resembles a Boltzmann-Gibbs equation and can be found by a globally convergent numerical algorithm. We further show that the minimax EP is the maximum uncertainty about the input that remains after observing the output. Finally, we extend the analysis to the continuous-time regime, showing that the minimax instantaneous EP diverges, while the corresponding finite-time minimax EP has a universal short-time scaling set by the largest escape rate of the dynamics.
Comments6 pages, 3 figures, 16 pages of Supplemental Material
