Beyond Point Particles -- Extended Structural Dynamics and the H Theorem

TL;DR

This paper introduces an extended structural dynamics framework that incorporates particle orientation and internal structure, providing a deterministic geometric basis for entropy production and the Second Law, extending classical mechanics and justifying molecular chaos.

Contribution

It develops a Hamiltonian-preserving extended dynamics model that explains entropy production and irreversibility through geometric instability, addressing limitations of point-particle theories.

Findings

Dual mechanisms for entropy production identified: collisional and geometric.

Geometric instability leads to unstable entropy-decreasing trajectories.

Provides a structural basis for the Second Law of thermodynamics.

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.