2008/03/09 by P. Visco, Paolo Visco, Frédéric van Wijland +3 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Gas Dynamics and Kinetic Theory #Phase Equilibria and Thermodynamics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.77.041117
published as Phys. Rev. E 77, 041117 (2008) · 13 pages, 12 figures
arxiv created 2008/03/09 · openalex publication_date 2008/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We investigate the probability distribution functions of the free flight time and of the number of collisions in a hard-sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit, which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex, Phys. Rev. E 69, 11303 (2004)]. We exploit this analogy to construct a Monte Carlo-like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are compared with the results of molecular dynamics simulations and the direct simulation Monte Carlo technique. An excellent agreement is reported.