On true relaxation statistics in gases

TL;DR

This paper demonstrates that in gases, the true collision statistics differ from classical assumptions, leading to a power-law decay in particle velocity relaxation, challenging traditional kinetic theory models.

Contribution

It reveals that collision probabilities are inherently random, resulting in a power-law relaxation behavior, and provides an estimate for its exponent based on simple kinematic reasoning.

Findings

Collision statistics differ from Boltzmann's molecular chaos assumptions.

Particle velocity relaxation follows a power-law asymptotic.

An estimate for the relaxation exponent is proposed.

Abstract

By example of a particle interacting with ideal gas, it is shown that statistics of collisions in statistical mechanics at any degree of the gas rarefaction qualitatively differs from that conjugated with Boltzmann's hypothetical molecular chaos and kinetic equation. In reality, probability of the particle collisions in itself is random, which results in power-law asymptotic of the particle velocity relaxation. An estimate of its exponent is suggested basing on simple kinematic reasonings