Title: Bridging Causality and Non-Equilibrium Thermodynamics via Hamiltonian Causal Models

Abstract: Standard causal models struggle to adequately address physical temporal phenomena, particularly when dealing with interventions along trajectories, nonstationary induced laws, path-dependent effects, and dynamics-mediated feedback. To overcome these limitations, we present Hamiltonian Causal Models (HCMs), a framework operating at the trajectory level. In this approach, observed variables engage with local environments, while interventions function as controls for Hamiltonian mechanisms. HCMs distinguish between immutable equations of motion and mechanisms susceptible to intervention, defining causal effects as the differences between interventional path laws.

A primary impetus for developing HCMs is their inherent compatibility with non-equilibrium thermodynamics. Entropy production serves as a central causal observable by quantifying process irreversibility. Crucially, it can be estimated from data and reveals causal effects during system evolution that remain undetected by standard average treatment effect measures, including their endpoint and cumulative variants. Consistent with physical principles, our model posits that cause and effect are not fundamental primitives relating two random variables; rather, they emerge from the non-invertibility of the thermodynamic arrow. By aligning the terminology of statistical causal models with non-stationary thermodynamics, this work provides novel methodologies for characterizing causality across a broad spectrum of physical systems.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC