H-theorem provides a microscopic foundation of the Second Law of Thermodynamics and is therefore essential to establishing statistical physics, but at the same time, H-theorem has been subject to controversy that in part persists till this day. To better understand H-theorem and its relation to the arrow of time, we study the equilibration of randomly oriented and positioned hard disks with periodic boundary conditions. Using a model based on the DeepSets architecture, which imposes permutation invariance of the particle labels, we train a model to capture the irreversibility of the H-functional.

翻译：H定理为热力学第二定律提供了微观基础，因而对建立统计物理学至关重要，但与此同时，H定理一直存在争议，部分争议甚至延续至今。为了更好地理解H定理及其与时间箭头的关联，我们研究了具有周期性边界条件的随机朝向与随机位置硬质圆盘的平衡过程。通过采用基于DeepSets架构的模型——该架构强制粒子标签的置换不变性——我们训练了一个模型以捕捉H泛函的不可逆性。