The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

摘要: In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions (S N -CDS). The problem posed in framework of ab initio S -CDS recently developed. It shown that Liouville equation SN-CDS admits an solution N-body probability density function (PDF). This factorized terms i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, denoted here as occupation coefficients. latter found depend functionally only on PDFs each remaining particles belonging -CDS. Furthermore, proved obey a well-defined equation, referred Master kinetic equation. takes into account occurrence configuration-space correlations due finite size extended particles, while depending same only. asymptotic approximation holds validity Boltzmann-Grad limit, recover sense customary Boltzmann Finally, critical analysis presented original and modified versions Enskog well some non-linear approaches formulated past dense granular gases. Their conditions main differences respect present theory pointed out.