Expressions for the energy density and evolved heat in the electrodynamics of a dispersive and absorptive medium

The question of the expressions for the energy density $W$ and evolved heat (dissipation) $Q$ in the electrodynamics of a dispersive and absorptive medium is discussed. Attention is concentrated on explaining the fact that $W$ and $Q$ are not expressed, generally speaking, in terms of the complex dielectric permittivity $\varepsilon(\omega)$. This statement is illustrated with the example of a medium consisting of a collection of oscillators and with the example of the simplest model of a plasma. A convenient expression for the energy density of a field with arbitrary time dependence in a transparent medium is obtained in the Appendix. A derivation of the high-frequency average of $(1/4\pi)\partial\mathbf{D}/\partial t\mathbf{E}$ for a quasi-monochromatic field in an absorptive dispersive medium is also given there.