Dynamical virial relations and invalidity of the Boltzmann kinetic equation

TL;DR

This paper derives exact relations linking distribution functions in low-density gases, demonstrating that the Boltzmann kinetic equation is invalid for spatially non-uniform gas evolutions, challenging a fundamental assumption in kinetic theory.

Contribution

It introduces a sequence of exact relations that show the inapplicability of the Boltzmann equation in non-uniform gas dynamics, contradicting traditional assumptions.

Findings

Exact relations connect distribution functions and their density derivatives.

Boltzmann equation's validity is challenged in non-uniform gas evolution.

Molecular chaos assumption is shown to be invalid in this context.

Abstract

A sequence of exact relations is found which connect one- and many-particle time-dependent distribution functions of low-density gas with their derivatives in respect to mean density. It is shown that, at least in the context of spatially non-uniform gas evolutions, these relations forbid the "molecular chaos propagation" and imply inapplicability of the Boltzmann kinetic equation even under the Boltzmann-Grad limit and regardless of degree of the non-uniformity.