The Vlasov equation and entropy

E. E. Perepelkin, B. I. Sadovnikov, N. G. Inozemtseva

Published 2017-02-15Version 1

It is well-known that the expression \[m\left\langle {\dot{\vec{v}}} \right\rangle =\vec{F}\] is used at solving the Vlasov equation. This work shows that in general case \[m\left\langle {\dot{\vec{v}}} \right\rangle \ne m\frac{d}{dt}\left\langle {\vec{v}} \right\rangle =\vec{F}.\] It is shown that using substitution \[m\left\langle {\dot{\vec{v}}} \right\rangle =\vec{F}\] narrows the class of the Vlasov equation as it corresponds to constant entropy systems. An equation form for the growing and constant entropy has been obtained.