Casimir energy dissipation in media at rest

From classical electrodynamics the energy dissipation per unit volume in a dispersive nonmagnetic medium is known to be equal to ωϵ″(ω) 〈E²〉, where ϵ″ denotes the imaginary part of the permittivity. The present work calculates the energy dissipation per unit surface area when two semi-infinite homogenous slabs are separated by a gap a. Only the gap-induced part of the dissipation is taken into account, so that the effect may be called a Casimir dissipative effect. Subtracting off the formal T = 0 expression the net dissipation is found to be negative. This reflects the fact that the dissipation in the presence of a gap is less than it would be in the case of a single homogeneous medium (i.e., a = ∞).