Geometric Irreversibility - Enriching Lanford's Theorem with Orientational and Deformable Degrees of Freedom

Patrick BarAvi

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arXiv · 2505.09650

Geometric Irreversibility - Enriching Lanford's Theorem with Orientational and Deformable Degrees of Freedom

Patrick BarAvi

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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.

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Patrick BarAvi. 2025-05-13. Geometric Irreversibility - Enriching Lanford's Theorem with Orientational and Deformable Degrees of Freedom. https://arxiv.org/abs/2505.09650

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