Reversible and irreversible processes in dispersive/dissipative optical media: Electro-magnetic free energy and heat production

We solve the problem addressed by Landau and Lifshitz in 1958, and Oughstun and Sherman of determining the dynamical losses in a purely dissipative dielectric media. We develop concrete notions of macroscopic free energy and losses as energy which is reversible and irreversible, respectively, in the medium-field interaction. We define the reversible and irreversible energies and outline the derivation of said quantities. We examine the implications of our definition and it's auxiliary quantity, the reversal field, for the single Lorentz oscillator model of a medium. We show that for this model the reversible energy reduces to the sum of the kinetic and potential energy, as found by Loudon. We note that in general, the sum of the kinetic and potential energies is greater than the reversible energy. We show that the reversible and irreversible energy have the characteristics classically defining free energy and heat.