Ideal gas · Collision dynamics
An Ideal Gas Can Remember Its Collisions
Main claim
A light tracer in a sufficiently dense ideal gas can develop a negative velocity autocorrelation because it repeatedly collides with the same gas particle. Even the simplest gas can retain a short-lived memory when the same two particles meet more than once.
Problem
Brownian motion is often modeled by averaging many molecular impacts into Gaussian random noise. At short times, however, a small and light tracer has experienced only a limited number of collisions. Even in an ideal gas with no fluid-fluid interactions, it was unclear whether those discrete events could create memory that the usual stochastic description misses.
Approach
We carried out event-driven hard-sphere simulations while varying tracer mass and gas density. Mean-square displacement, the non-Gaussian parameter, and velocity autocorrelation were measured. To identify the mechanism, we analyzed waiting times and correlations across successive collision events, including whether the tracer met the same gas particle more than once.
What we found
Heavy tracers behave close to a Gaussian stochastic process, but a light tracer in a sufficiently dense gas develops a negative velocity autocorrelation. A model based only on independent successive collisions cannot reproduce it. The negative correlation is generated mainly by multiple collisions between the tracer and the same gas particle, which retain information about earlier motion.
Why it matters
The result demonstrates that dynamical memory does not require static structure, hydrodynamic interactions, or a complex solvent. It can be assembled directly from a short collision history. This helps define when continuum or Gaussian-noise models are justified and when molecular collision statistics must be kept explicitly.
Keywords
ideal gas, tracer dynamics, collision correlation, velocity autocorrelation, event-driven simulation.
Paper
, “Short-time dynamics of a tracer in an ideal gas,” Physical Review E 102, 032104 (2020).