Brownian Motion as Deterministic Arithmetic Friction and the Death of the Wiener Process
{"We":[0,49],"present":[1],"the":[2,9,24,28,36,72,77,95],"computational":[3],"and":[4,16,27,41,43,122],"theoretical":[5],"framework":[6],"for":[7],"extending":[8],"Computational":[10],"Finitism":[11],"paradigm":[12],"to":[13,71,103],"statistical":[14],"mechanics":[15],"diffusion.":[17],"Standard":[18],"physics":[19],"models":[20],"Brownian":[21],"motion":[22],"via":[23],"Langevin":[25],"equation":[26],"Wiener":[29],"process,":[30],"relying":[31],"on":[32],"two":[33],"foundational":[34],"fallacies:":[35],"continuum":[37],"assumption":[38],"(infinitesimal":[39],"time":[40],"space)":[42],"ontological":[44],"randomness":[45],"(true":[46],"Gaussian":[47],"noise).":[48],"demonstrate":[50],"that":[51,81,94,112],"diffusion":[52,114],"emerges":[53],"naturally":[54],"from":[55],"a":[56,107,118,126],"strictly":[57],"deterministic,":[58],"finite-state":[59],"Modulo-9":[60],"cellular":[61],"automaton":[62],"without":[63],"any":[64],"stochastic":[65],"variables.":[66],"By":[67],"coupling":[68],"particle":[69],"displacement":[70],"local":[73],"topological":[74],"state":[75,120],"of":[76,87],"substrate,":[78],"we":[79,92],"prove":[80],"\\"thermal":[82],"kicks\\"":[83],"are":[84],"actually":[85],"manifestations":[86],"deterministic":[88,127],"arithmetic":[89],"friction.":[90],"Crucially,":[91],"show":[93],"Mean":[96],"Squared":[97],"Displacement":[98],"(MSD)":[99],"does":[100],"not":[101],"diverge":[102],"infinity,":[104],"but":[105],"hits":[106],"hard,":[108],"predictable":[109],"plateau,":[110],"proving":[111],"macroscopic":[113],"is":[115],"bounded":[116],"by":[117],"finite":[119],"space":[121],"must":[123],"eventually":[124],"enter":[125],"limit":[128],"cycle.":[129]}
Authors
- Néstor E Ramos (ORCID: https://orcid.org/0009-0007-3211-9347)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-21
- DOI
- https://doi.org/10.5281/zenodo.22879740
- Primary Topic
- Cellular Automata and Applications
- Type
- preprint