A truth about Brownian motion in gases and in general

TL;DR

This paper argues that the long-term thermal motion of gas molecules and electrons is fundamentally non-Gaussian, challenging traditional models, and provides a simple proof based on microscopic determinism and reversibility.

Contribution

It introduces a straightforward proof demonstrating the non-Gaussian nature of long-term Brownian motion in gases, based solely on microscopic dynamics and virial expansion.

Findings

Long-term Brownian motion is non-Gaussian.

Microscopic determinism and reversibility imply non-Gaussian statistics.

Virial expansion supports the non-Gaussian behavior.

Abstract

Real thermal motion of gas molecules, free electrons, etc., at long time intervals (much greater than mean free-flight time) possesses, contrary to its popular mathematical models, essentially non-Gaussian statistics. A simple proof of this statement is suggested basing on only the determinism and reversibility of microscopic dynamics and besides incidentally derived virial expansion of a path probability distribution of molecular Brownian particle.