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

{"FINDING:":[0],"Hilbert's":[1],"Sixth":[2],"Problem":[3],"—":[4,12,94],"the":[5,40,63,117,132,148],"axiomatization":[6],"of":[7,20,101,108,147],"physics":[8],"via":[9],"statistical":[10],"mechanics":[11],"saw":[13],"a":[14,28],"major":[15],"2025":[16],"breakthrough:":[17],"rigorous":[18],"derivation":[19],"fluid":[21],"dynamics":[22],"(Euler/Navier-Stokes)":[23],"from":[24,31,43,90,111],"particle":[25],"dynamics,":[26],"plus":[27],"radical":[29],"\\"physics":[30],"no":[32,95],"physics\\"":[33],"proposal.":[34],"|":[35,104],"MATH:":[36],"The":[37,75,106],"core":[38],"is":[39],"hydrodynamic":[41],"limit:":[42],"N-particle":[44],"Liouville":[45],"equation":[46],"(∂ₜμ_N":[47],"+":[48,79,83],"{μ_N,":[49],"H_N}":[50],"=":[51,81],"0)":[52],"to":[53,136],"continuum":[54],"equations.":[55],"Key":[56],"constants:":[57],"Boltzmann's":[58],"k_B,":[59],"Planck's":[60],"ħ,":[61],"and":[62,125],"scaling":[64,126],"limit":[65],"N→∞,":[66],"ε→0":[67],"(mean":[68],"free":[69],"path)":[70],"with":[71],"εN^{1/d}":[72],"→":[73],"const.":[74],"Navier-Stokes":[76],"equation:":[77],"∂ₜu":[78],"(u·∇)u":[80],"−∇p":[82],"ν∇²u,":[84],"where":[85],"ν":[86],"(kinematic":[87],"viscosity)":[88],"emerges":[89],"microscopic":[91,102,112],"collision":[92,119],"integrals":[93],"new":[96],"fundamental":[97],"constant,":[98],"only":[99],"ratios":[100],"scales.":[103],"CONNECTION:":[105],"emergence":[107],"macroscopic":[109,133],"equations":[110],"symmetries":[113,127],"mirrors":[114],"root-system/lattice":[115],"structure:":[116],"Boltzmann":[118],"operator's":[120],"invariance":[121],"under":[122],"Galilean,":[123],"rotational,":[124],"(SO(3),":[128],"translations,":[129],"dilations)":[130],"forces":[131],"stress":[134],"tensor":[135],"be":[137],"isotropic":[138],"Author:":[139],"Andrew":[140],"Stewart":[141],"Caldin,":[142],"Independent":[143],"Researcher,":[144],"UK.":[145],"Part":[146],"E8":[149],"Intelligence":[150],"Research":[151],"series.":[152],"Platform:":[153],"e8intelligence.com":[154]}

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22762223
Primary Topic
Statistical Mechanics and Entropy
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
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
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.