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Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Counterfactual identification and bounds · 0 citations (OpenAlex)

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Introduces Hamiltonian Causal Models (HCMs), a trajectory-level causal framework where interventions act as controls of Hamiltonian mechanisms, and shows entropy production witnesses causal effects and can recover parents in cyclic Langevin systems.

Problem

Standard causal models struggle with time-dependent interventions acting along trajectories, nonstationary induced laws, path-dependent effects, and feedback in physical temporal systems; the link between causality and non-equilibrium thermodynamic irreversibility is not formalized.

Approach

Model observed variables each coupled to an unobserved thermal bath under a controlled Hamiltonian; interventions modify the Hamiltonian mechanisms (not the equations of motion), causal effects are discrepancies between interventional path laws, and node-level entropy production (projected and channel-local) serves as a data-estimable causal witness and parent-detection signal.

Key results

• In the same-endpoint setting, endpoint ATE is -0.012 (CI [-0.037, +0.012]) while projected entropy production contrast is -0.366 ± 0.001 (p=2.3e-6).
• On random cyclic ER graphs (n=15), parent recovery via local EP response achieves F1 of 0.839 (Bilinear), 0.858 (Sigmoid), 0.825 (Cubic) with recall around 0.96-0.97.
• Cumulative ATE is +0.002 (CI [-0.062, +0.067]) in the reversed-pulse setting while projected EP contrast is -0.417 ± 0.017.

Limitations

• Extension to general temporal SCMs with non-gradient drifts is not covered.
• Experiments are small synthetic simulations; no real physical data.
• Projected EP witnesses only directed-path effects, not direct parenthood; parent detection needs full-state local EP and faithfulness assumptions.

Experimental setup

Datasets: synthetic controlled overdamped Langevin trajectories on random cyclic Erdős–Rényi graphs (n=15)

Benchmarks: synthetic linear oscillator chain (same endpoints) synthetic hidden-mediator system (reversed pulses) random cyclic ER graphs for parent recovery

Metrics: ATE F1 precision recall local SHD p-value

Baselines: endpoint ATE cumulative ATE

Builds on: structural causal models phenomenological causality stochastic thermodynamics NEEP entropy production estimator Caldeira-Leggett model

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