2022/03/02 by Farida Kachapova, Kachapova, Farida, Ilias Kachapov +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #82C03 (Primary) 82M60 (Secondary) #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Education and Methodologies
paper · pdf · doi:10.48550/arxiv.2203.01390
openalex publication_date 2022/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in classical mechanics, here we use probabilistic properties of particle movement 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.