Teaching world models to respect physics through energy

World models used in reinforcement learning typically learn dynamics without physical constraints, leading to unrealistic predictions. This work applies Port-Hamiltonian mechanics to enforce energy conservation and dissipation in latent space, computing explicit Hamiltonian functions from observations and using energy gradients to regularize policy learning. On visual control benchmarks, the approach achieves higher asymptotic returns, tighter alignment between imagined and real rewards, and 4–8% smaller latent representations, while cutting energy consumption by up to 7.8%. Intended for researchers building sample-efficient RL agents in continuous control; no code or model release mentioned in the abstract.