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 e(ω). 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 (1/4π)∂D/∂t for a quasi-monochromatic field in an absorptive dispersive medium is also given there.