Brownian Motion as Deterministic Arithmetic Friction and the Death of the Wiener Process

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Authors

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
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preprint

Brownian Motion as Deterministic Arithmetic Friction and the Death of the Wiener Process

Néstor E Ramos
Zenodo (CERN European Organization for Nuclear Research)
Cellular Automata and Applications
preprint

Brownian Motion as Deterministic Arithmetic Friction and the Death of the Wiener Process

Néstor E Ramos
preprint en

Abstract

We present the computational and theoretical framework for extending the Computational Finitism paradigm to statistical mechanics and diffusion. Standard physics models Brownian motion via the Langevin equation and the Wiener process, relying on two foundational fallacies: the continuum assumption (infinitesimal time and space) and ontological randomness (true Gaussian noise). We demonstrate that diffusion emerges naturally from a strictly deterministic, finite-state Modulo-9 cellular automaton without any stochastic variables. By coupling particle displacement to the local topological state of the substrate, we prove that "thermal kicks" are actually manifestations of deterministic arithmetic friction. Crucially, we show that the Mean Squared Displacement (MSD) does not diverge to infinity, but hits a hard, predictable plateau, proving that macroscopic diffusion is bounded by a finite state space and must eventually enter a deterministic limit cycle.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities, Peace, Justice and strong institutions
Cellular Automata and Applications
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