# Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models

arXiv: https://arxiv.org/abs/2606.04822 · HTML: https://mlsanity.com/paper/2606.04822/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 71 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)
- [Time series experiments and causal estimands: exact randomization tests and trading](https://mlsanity.com/paper/1706.07840/) (2017)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [Dynamic Structural Causal Models](https://mlsanity.com/paper/2406.01161/) (2024)
- [Learning entropy production via neural networks](https://mlsanity.com/paper/2003.04166/) (2020)
- [Prediction-Powered Causal Inferences](https://mlsanity.com/paper/2502.06343/) (2025)
- [Estimating Time-Varying Causal Excursion Effect in Mobile Health with Binary Outcomes](https://mlsanity.com/paper/1906.00528/) (2019)
- [On Geometry of Information Flow for Causal Inference](https://mlsanity.com/paper/2002.02078/) (2020)
- [Exploratory Causal Inference in SAEnce](https://mlsanity.com/paper/2510.14073/) (2025)
- [Causal identification for continuous-time stochastic processes](https://mlsanity.com/paper/2211.15934/) (2022)

## Abstract (arXiv)

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.