用神经网络从微观粒子数据中自动发现时间箭头
Machine Learning the H-theorem
- 构建可置换不变的深度集神经网络，仅通过时序排序训练
- 模型学习到的标量与玻尔兹曼熵函数高度相关
- 为热力学第二定律提供数据驱动的微观解释，适合物理与机器学习交叉研究者
H定理为热力学第二定律提供了微观基础，在统计物理中占据核心地位。然而其与微观可逆性之间的关系仍存在概念上的微妙之处。为探究时间箭头能否直接从微观数据中推断，我们研究了周期性方盒中随机初始化硬球系统的弛豫过程。基于DeepSets架构构建了一个排列不变的神经网络，仅训练其将后续状态赋予比先前状态更高的标量值。我们将学习到的标量与玻尔兹曼H泛函进行比较，评估动力学本身在多大程度上使模型趋于符合H定理所暗示的结构。
原文摘要 · Abstract (English)
The H-theorem provides a microscopic foundation for the Second Law of Thermodynamics and therefore occupies a central place in statistical physics. At the same time, its relation to microscopic reversibility has remained conceptually subtle. To investigate how an arrow of time may be inferred directly from microscopic data, we study the relaxation of randomly initialized hard disks in a periodic box. We construct a permutation-invariant neural network based on the DeepSets architecture. The model is trained only to assign later states a larger scalar value than earlier states. We compare the learned scalar with the Boltzmann H-functional and assess to what extent the dynamics alone lead the model toward the structure implied by the H-theorem.
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