Derivation of the particle dynamics from kinetic equations |
| |
Authors: | A S Trushechkin |
| |
Institution: | 1.Steklov Mathematical Institute,Russian Academy of Sciences,Moscow,Russia;2.National Research Nuclear University “MEPhI”,Moscow,Russia |
| |
Abstract: | The microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov are considered. The fact that the time-irreversible
kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the
reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If
the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions
belong to the class of continuously differentiable functions, then the equation is irreversible. Also, the so called approximate
microscopic solutions are constructed. These solutions are continuous and they are reversible on bounded time intervals. This
analysis suggests a way to reconcile the time-irreversible kinetic equations with the timereversible particle dynamics. Usually
one tries to derive the kinetic equations from the particle dynamics. On the contrary, we postulate the Boltzmann-Enskog equation
or another kinetic equation and treat their microscopic solutions as the particle dynamics. So, instead of the derivation
of the kinetic equations from the microdynamics we suggest a kind of derivation of the microdynamics from the kinetic equations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|