Plasma model and Drude model permittivities in Lifshitz formula

At the physical level of rigour it is shown that there are no substantial theoretical arguments in favour of using either plasma mode permittivity or Drude model permittivity in the Lifshitz formula. The decision in this question rests with the comparison of theoretical calculations with the experiment. In the course of the study the derivation of the fluctuation-dissipation theorem is proposed where it is displayed clear at which reasoning stage and in what way the dissipation is taken into account. In particular it is shown how this theorem works in the case of the system with reversible dynamics, that is when dissipation is absent. Thereby it is proved that explicit assertion according to which this theorem is inapplicable to systems without dissipation is erroneous. The research is based on making use of the rigorous formalism of equilibrium two-time Green functions in statistical physics at finite temperature.