Derivation from Kac’s Master Equation of the Stochastic Laws for Simulating Molecular Collisions

Abstract

Belotserkovskiy and Yanitskiy proposed stochastic laws for simulating molecular collisions in gas; these laws are consistent with the assumptions on which Kac’s master equation is built up. Firstly, it is shown that the laws can be derived directly from Kac’s master equation by use of the stochastic solution method recently proposed by the author. Secondly, by use of the laws the solution of Kac’s master equation is obtained and compared with the known exact solution of the Boltzmann equation. If the number of simulated molecules greater than about 40 is used, the obtained solution agrees with the exact solution.