Asymptotic orderings and approximations of the Master kinetic equation for large hard spheres systems
Abstract
In this paper the problem is posed of determining the physicallymeaningful asymptotic orderings holding for the statistical description of a large Nbody system of hard spheres, i.e., formed by N ≡1/ɛ ≫ 1 particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto et al., 20132016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the 1body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of ɛ for all the physicallyrelevant parameters. The goal is that of identifying the relevant physicallymeaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by smallsize or finitesize identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of ɛ.
 Publication:

Physics Letters A
 Pub Date:
 May 2017
 DOI:
 10.1016/j.physleta.2017.03.001
 arXiv:
 arXiv:1701.01834
 Bibcode:
 2017PhLA..381.1484T
 Keywords:

 Classical statistical mechanics;
 Kinetic theory;
 Exact and asymptotic kinetic equations;
 Hardsphere classical dynamical system;
 Physics  Classical Physics
 EPrint:
 doi:10.1016/j.physleta.2017.03.001