Non Poissonian statistics in a low density fluid

TL;DR

This paper investigates the collision statistics of a tagged particle in a low density fluid, revealing deviations from Poissonian behavior and exponential free flight times, supported by analytical calculations and molecular dynamics simulations.

Contribution

It demonstrates that in low density fluids, collision counts do not follow Poisson statistics and free flight times are not purely exponential, challenging naive assumptions.

Findings

Collision statistics deviate from Poisson law

Free flight time distribution is not exponential

Analytical predictions match molecular dynamics simulations

Abstract

Our interest goes to the collisional statistics in an arbitrary interacting fluid. We show that even in the low density limit and contrary to naive expectation, the number of collisions experienced by a tagged particle in a given time does not obey Poisson law, and that conversely, the free flight time distribution is not a simple exponential. As an illustration, the hard sphere fluid case is worked out in detail. For this model, we quantify analytically those deviations and successfully compare our predictions against molecular dynamics simulations.