Elements of Formal Probabilistic Mechanics

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.