Beyond Point Particles -- Extended Structural Dynamics and the H Theorem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911416886231040 |
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| author | BarAvi, Patrick |
| author_facet | BarAvi, Patrick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09650 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond Point Particles -- Extended Structural Dynamics and the H Theorem BarAvi, Patrick Statistical Mechanics History and Philosophy of Physics 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. |
| title | Beyond Point Particles -- Extended Structural Dynamics and the H Theorem |
| topic | Statistical Mechanics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2505.09650 |