Brownian particle in ideal gas: explicit density expansions, conditional probabilities, and amusing properties of molecular chaos

TL;DR

This paper derives explicit density expansions for a Brownian particle in an ideal gas, linking them to dynamical virial relations and exploring molecular chaos properties, including 1/f noise, through conditional probabilities.

Contribution

It provides the first explicit density expansions for non-equilibrium distributions of a Brownian particle in an ideal gas, connecting them to virial relations and molecular chaos analysis.

Findings

Explicit density expansions are derived and shown to satisfy dynamical virial relations.

The role of molecular chaos in non-equilibrium states and 1/f noise is clarified.

Conditional probabilities and averages are used to analyze molecular chaos properties.

Abstract

Explicit density expansions of non-equilibrium probability distribution functions for molecular Brownian particle in ideal gas are obtained in original form what visually implies (is exact solution to) the previously established dynamical virial relations. Role of these relations in unbiased analysis of molecular chaos properties in many-particle statistical mechanics, including the mobility 1/f noise, is newly investigated in clear terms of conditional probabilities and averages.