Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models

2026-06-03

AI Summary

Traditional causal models struggle to capture trajectory-level interventions, non-stationarity, path dependence, and dynamical feedback inherent in physical time-series systems. This work proposes Hamiltonian Causal Models (HCMs), which disentangle immutable equations of motion from intervenable mechanisms at the trajectory level, defining causal effects through differences in path laws under intervention. For the first time, it unifies statistical causal inference with nonequilibrium thermodynamics by introducing entropy production as a fundamental causal observable, thereby revealing evolving causal structures invisible to conventional average treatment effects. The framework enables data-driven estimation of entropy production and identification of causal directions induced by the thermodynamic arrow of time, establishing a novel paradigm for trajectory-level causal modeling across a broad class of physical systems.

Abstract

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.

Problem

• causal modeling
• non-equilibrium thermodynamics
• trajectory-level interventions
• path-dependent effects
• entropy production

Innovation

• Hamiltonian Causal Models
• non-equilibrium thermodynamics
• entropy production
• trajectory-level causality
• interventional path laws