On statistics of molecular chaos

TL;DR

This paper demonstrates that the BBGKY equations reveal persistent many-particle correlations affecting particle path distributions, challenging the classical kinetic theory even at low gas densities.

Contribution

It establishes exact relations between path probabilities, their derivatives, and many-particle correlations, showing classical kinetics is insufficient.

Findings

Correlations of all orders significantly influence particle path evolution.

Classical kinetic theory does not emerge in the low-density limit.

Exact relations between path distributions and correlations are derived.

Abstract

It is shown that the BBGKY equations for a particle interacting with ideal gas imply exact relations between probability distribution of path of the particle, its derivatives in respect to the gas density and irreducible many-particle correlations of gas atoms with the path. These relations visualize that the correlations of any order always significantly contribute to evolution of the path distribution, so that the exact statistical mechanics theory does not reduce to the classical kinetics even in the low-density (or Boltzmann-Grad) limit.