Is the mean free path the mean of a distribution?

TL;DR

This paper clarifies that Maxwell's mean free path in a dilute hard-sphere gas is both the average of the collision time product and the statistical mean of free path lengths, highlighting a fundamental connection.

Contribution

It demonstrates that Maxwell's mean free path equals the statistical mean of free path lengths, linking a classical kinetic theory quantity to a distribution-based measure.

Findings

Maxwell's mean free path equals the statistical mean of free path lengths.

The mean free path is both a kinetic average and a distribution mean.

Clarifies the interpretation of the mean free path in kinetic theory.

Abstract

We bring attention to the fact that Maxwell's mean free path for a dilute hard-sphere gas in thermal equilibrium, $(\sqrt{2}\sigma n)^{-1}$, which is ordinarily obtained by multiplying the average speed by the average time between collisions, is also the statistical mean of the distribution of free path lengths in such a gas.