论文标题
当您无法计数时，请采样！可计算的熵超出盆地体积的平衡
When you can't count, sample! Computable entropies beyond equilibrium from basin volumes
论文作者
论文摘要
在统计力学中，测量了可用状态及其概率的数量，因此可以预测平衡处物理系统的宏观特性。这种预测能力取决于鲍尔茨曼分布给出的观察系统状态的先验概率的知识。不幸的是，平衡统计力学的成功很难从平衡中复制出来，在这种情况下，观察状态的先验概率通常是未知的，从而排除了常规工具的幼稚应用。在过去的十年中，由于在高维盆地的吸引力盆地量的计算方面取得了重大的方法学进步，因此发生了令人兴奋的发展，可以直接对Athermal和非平衡系统状态的熵和密度进行直接数值估计。在这里，我们提供了有关这些方法的详细说明，强调了这些估计中所面临的挑战，对此事的最新进展以及未来工作的有希望的方向。
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity hinges on the knowledge of the a priori probabilities of observing the states of the system, given by the Boltzmann distribution. Unfortunately, the successes of equilibrium statistical mechanics are hard to replicate out of equilibrium, where the a priori probabilities of observing states are in general not known, precluding the naïve application of usual tools. In the last decade, exciting developments have occurred that enable the direct numerical estimation of the entropy and density of states of athermal and non-equilibrium systems, thanks to significant methodological advances in the computation of the volume of high-dimensional basins of attraction. Here, we provide a detailed account of these methods, underscoring the challenges that lie in such estimations, recent progress on the matter, and promising directions for future work.
