Limits of Collective Description and Their Consequences for Landau Damping

By application of the concept of collective description to a fully ionized gas, Vlasov's equation follows from Liouville's theorem. We want to investigate to what extent the statistical collective procedure describes correctly the behavior of the single system under consideration. Therefore a criterion for the validity of the collective approach is deduced by comparison of the Vlasov equation with the exact individual description. The result is exemplified by an application to Landau's theory of damping of plasma oscillations.