Extended Structural Dynamics -- Emergent Irreversibility from Reversible Dynamics

The emergence of irreversibility in isolated, deterministic systems remains a central problem in the foundations of statistical mechanics. Traditional approaches, such as Boltzmann's H-theorem and Lanford's derivation of the Boltzmann equation, rely on probabilistic assumptions and are constrained to dilute gases and short timescales. In this work, we introduce Extended Structural Dynamics (ESD), a deterministic framework in which irreversibility arises from the internal geometry of structured particles. In ESD, particles possess finite size and internal degrees of freedom, such as rotation and vibration, that are dynamically coupled to translational motion. This coupling induces instability, nonlinear feedback, and chaotic mixing in the extended phase space, even under time-reversal symmetric laws. We show that equilibrium states exponentially dominate the accessible volume of phase space, while constrained configurations (e.g., pure rotation) form measure-zero subsets. This yields a geometric derivation of entropy growth, with reversal probabilities suppressed as Prev and recurrence times scaling as Trec. These results address the Loschmidt and Zermelo paradoxes without coarse-graining, randomness, or fine-tuning. We further extend the model to charged systems (cESD), where long-range electromagnetic interactions drive continuous structural coupling. ESD thus provides a deterministic and testable mechanism for emergent thermodynamic behavior, with applications ranging from mesoscopic systems to the cosmological arrow of time.