Research Article Open Access

Elements of Formal Probabilistic Mechanics

Farida Kachapova1 and Ilias Kachapov2
  • 1 Auckland University of Technology, New Zealand
  • 2 University of Auckland, New Zealand


In this study model of particle motion on a three-dimensional lattice is created using discrete random walk with small steps. A probability space of the particle trajectories is rigorously constructed. Unlike deterministic approach in classical mechanics, here probabilistic properties of particle movement are used to formally derive analogues of Newton’s first and second laws of motion. Similar probabilistic models can potentially be applied to justify laws of thermodynamics in a consistent manner.

Journal of Mathematics and Statistics
Volume 18 No. 1, 2022, 16-26


Submitted On: 7 August 2021 Published On: 18 March 2022

How to Cite: Kachapova, F. & Kachapov, I. (2022). Elements of Formal Probabilistic Mechanics. Journal of Mathematics and Statistics, 18(1), 16-26.

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  • Newton’s Laws of Motion
  • Particle Trajectory on Lattice
  • Random Walk
  • Kolmogorov Extension Theorem