用哈密顿机制建模物理过程中的因果关系，揭示熵增的因果作用。
Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models
- 基于哈密顿机制构建轨迹级因果模型，分离运动方程与可干预项。
- 熵产生量可从数据估算，反映系统演化中不可逆的因果效应。
- 适合研究非平衡热力学与动态系统因果性的研究人员。
传统因果模型难以处理沿轨迹施加的干预、非平稳诱导规律、路径依赖效应及动力学反馈。本文提出哈密顿因果模型（HCM），在轨迹层面建模观测变量与局部环境的交互，将干预视为对哈密顿机制的控制。HCM将不变的运动方程与可干预机制分离，并将因果效应定义为干预路径律与对照路径律之间的差异。其核心动机在于自然对接非平衡热力学：熵产生量化过程不可逆性，是关键因果可观测量——可由数据估计，且能捕捉终点和累积平均处理效应无法察觉的演化中因果效应。如同物理规律，因果关系并非随机变量间的原始关系，而是源于热力学箭头的不可逆性。本工作统一统计因果模型与非平稳热力学语言，为多种物理系统提供新因果描述工具。
原文摘要 · Abstract (English)
Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate immutable equations of motion from intervenable mechanisms and define causal effects as discrepancies between interventional path laws. A key motivation for HCMs is their natural interface with non-equilibrium thermodynamics. Entropy production quantifies the irreversibility of a process and is a central causal observable: it is estimable from data and witnesses causal effects along the system's evolution that are invisible to endpoint and cumulative versions of the standard average treatment effect. As in physics, cause and effect are not primitives of the relation between two random variables but arise from the non-invertibility of the thermodynamic arrow. With this, our paper reconciles the language of statistical causal models and non-stationary thermodynamics, offering new tools to describe causality in a wide range of physical systems.
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