A lemma about molecular chaos

TL;DR

This paper derives exact relations in the statistical mechanics of a Brownian particle in an ideal gas, showing that many-particle correlations remain significant and prevent reduction to classical kinetics, even at low densities.

Contribution

It provides new exact relations linking path probabilities, derivatives, and correlations, challenging the classical kinetic theory assumptions.

Findings

Correlations contribute equally to path evolution.

Classical kinetics does not fully describe the system.

Exact relations hold for the BBGKY hierarchy.

Abstract

Solutions to the BBGKY hierarchy of equations for molecular Brownian particle in ideal gas are considered, and exact relations are derived between probability distribution of path of the particle, its derivatives in respect to gas density and irreducible many-particle correlations of gas atoms with the path. It is shown that all the correlations always give equally important contributions to evolution of the path distribution, and therefore the exact statistical mechanics theory does not reduce to classical kinetics even in the low-density limit.