Real-time determination of free energy and losses in optical absorbing media

We introduce notions of free energy and loss in linear, absorbing dielectric media which are relevant to the regime in which the macroscopic Maxwell equations are themselves relevant. As such we solve a problem eluded to by Landau and Lifshitz in 1958, and later considered explicitly by Barash and Ginzburg, and Oughtsun and Sherman. As such we provide physically-relevant real-time notions of "energy" and "loss" in all analogous linear dissipative systems.