Dispersion chain of Vlasov equations

TL;DR

This paper introduces a new infinite dispersion chain derived from the Vlasov equations, expanding the framework to include mixed higher order kinematical values with tensor form and conservation laws.

Contribution

It develops a novel dispersion chain of equations with tensor structure, extending the Vlasov chain to include arbitrary kinematical values and deriving related conservation laws.

Findings

Derived a new dispersion chain with tensor form

Established equations for mixed Boltzmann functions

Proved probability invariance for negative quasi-probability regions

Abstract

On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).