Abstract
A technique, by means of which closed markovian kinetic equations can be formally obtained from a Liouville-type equation, is presented. In this approach, a projection operator is defined in terms of three conditions, which are postulated as being necessary and sufficient conditions for the existence of an exact markovian equation. The formalism is applied to the BBGKY hierarchy of equations, and to the Liouville equation. In the former case, the Choh-Uhlenbeck equation for the single-particle distribution function is rederived without using the Bogoliubov“ansatz”, and in the latter case, the Prigogine-Résibois equation for the full-velocity distribution function is derived. This approach provides a basic mathematical structure which underlies these kinetic equations.
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