Rigorous Derivation of Fluid Dynamics from Particle Motion: A 2025 Breakthrough — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22762222
Primary Topic
Statistical Mechanics and Entropy
Type
preprint
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preprint

Rigorous Derivation of Fluid Dynamics from Particle Motion: A 2025 Breakthrough — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Statistical Mechanics and Entropy
preprint

Rigorous Derivation of Fluid Dynamics from Particle Motion: A 2025 Breakthrough — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Hilbert's Sixth Problem — the axiomatization of physics via statistical mechanics — saw a major 2025 breakthrough: rigorous derivation of fluid dynamics (Euler/Navier-Stokes) from particle dynamics, plus a radical "physics from no physics" proposal. | MATH: The core is the hydrodynamic limit: from N-particle Liouville equation (∂ₜμ_N + {μ_N, H_N} = 0) to continuum equations. Key constants: Boltzmann's k_B, Planck's ħ, and the scaling limit N→∞, ε→0 (mean free path) with εN^{1/d} → const. The Navier-Stokes equation: ∂ₜu + (u·∇)u = −∇p + ν∇²u, where ν (kinematic viscosity) emerges from microscopic collision integrals — no new fundamental constant, only ratios of microscopic scales. | CONNECTION: The emergence of macroscopic equations from microscopic symmetries mirrors root-system/lattice structure: the Boltzmann collision operator's invariance under Galilean, rotational, and scaling symmetries (SO(3), translations, dilations) forces the macroscopic stress tensor to be isotropic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Statistical Mechanics and Entropy
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Rigorous Derivation of Fluid Dynamics from Particle Motion: A 2025 Breakthrough — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS