A truth of molecular chaos

TL;DR

This paper investigates the BBGKY hierarchy for a particle in an ideal gas, revealing that many-particle correlations are always significant, challenging classical kinetic theory even at low densities.

Contribution

It uncovers exact identities linking path probabilities, derivatives, and correlations, demonstrating the non-reducibility of the theory to classical kinetics.

Findings

Correlations contribute equally to path evolution.

Classical kinetics does not hold at any gas density.

Exact identities connect path probabilities and correlations.

Abstract

The BBGKY hierarchy of equations for a particle interacting with an ideal gas is investigated. Principal properties of its solutions are disclosed, as exact identities which connect probability distribution of path of the particle, its derivatives in respect to gas density and irreducible many-particle correlations between gas molecules and the path. They show that all the correlations always give equally important contributions to evolution of the path distribution, and therefore the exact theory does not reduce to the classical kinetics even at arbitrary small gas density.