发表机构
Laboratoire de Physique de l’Ecole Normale Supérieure, CNRS, ENS and PSL Université, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎高等师范学院及PSL大学，索邦大学，巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究重新表述统计力学弛豫问题，以信号局域时间统计量为核心，结合有限自由度系统特性与损失函数，赋予熵学习解释，明确其平稳值依赖观测者可用信息。
AI 中文摘要
我们通过明确受弛豫支配的“操作”对象，重新表述了统计力学中的弛豫问题：即记录信号$Z(t)$的局域时间统计量。这些局域时间统计量是无时钟观测者在均匀随机时刻$\boldsymbol{\textit{t}_i}$（$i=1$到$M$）对观测值$\boldsymbol{\textit{Z}(t_i)}$进行观测所得的估计直方图。预测的对象是对未来新的、超出样本的测量结果读数的置信度，该读数的分布由被认为正确的数学模型推断得出。对于具有$N\boldsymbol{\textit{≥1}}$个自由度的有限有界系统，预测会发生全局不可逆弛豫，但存在特殊的初始条件。预测的形式取决于特定观测者可选择的某些损失函数。最后，熵被赋予了学习解释，即观测者与所考虑系统的未知过去之间的互信息，且在完全一般性下，其平稳值取决于可用信息。
英文摘要
We reformulate the relaxation problem in statistical mechanics by making explicit what are the \emph{operational} objects subject to relaxation: the local time statistics of the recorded signal $Z(t)$. These local time statistics are simply the estimated histograms of observations $\{Z(t_i)\}_{i=1}^M$ performed at uniformly random times $\{t_i\}_{i=1}^M$ by a clockless observer. The subject of prediction is a belief about a future fresh out-of-sample reading of a measurement outcome whose distribution is inferred from the mathematical model believed to be true. For finite bounded systems of $N\ge 1$ degrees of freedom global irreversible relaxation of predictions can occur but special initial conditions exist. The form of the predictions depends on certain loss functions whose choice is up to the particular observer. Finally, entropy is given a learning interpretation as mutual information between the observer and the unknown past of the system under consideration and, in complete generality, its stationary value depends on the information available.
Comments18 pages, 5 figures
