Beyond Point Particles -- Extended Structural Dynamics and the H Theorem
Abstract
We propose an extended structural dynamics framework that enriches classical mechanics by treating particle orientation and internal structure as fundamental phase-space coordinates. This extension preserves Hamiltonian structure and Liouville invariance while revealing two distinct mechanisms for entropy production: (i) collisional randomization through orientation-dependent scattering (generalizing Boltzmann), and (ii) continuous geometric instability arising from rotational-deformational coupling. We argue this dual-mechanism structure provides a dynamical justification for the molecular chaos assumption central to Boltzmann-Lanford derivations, particularly in regimes (dense systems, few bodies, structured particles) where classical point-particle theory fails. Recent mathematical advances (Deng, Hani & Ma 2024) extend Lanford's theorem to arbitrary times but still require molecular chaos as input and apply only to dilute gases. This extended structural framework addresses the complementary philosophical question: how can molecular chaos itself emerge from deterministic dynamics? We show that geometric instability in extended phase space makes entropy-decreasing trajectories dynamically unstable, offering a structural explanation for the Second Law. This reframes thermodynamic irreversibility as a geometric property of structured motion rather than a purely statistical postulate.
Cite
@article{arxiv.2505.09650,
title = {Beyond Point Particles -- Extended Structural Dynamics and the H Theorem},
author = {Patrick BarAvi},
journal= {arXiv preprint arXiv:2505.09650},
year = {2026}
}
Comments
Title and abstract updated