The autocorrelation of the thermally induced currents in infinite media

According to our recent modal representation, the origin of thermal radiation can be associated to the distribution of a finite number of current sources, independent one from the other, the Degrees of Freedom (DoF). Here we show that, if one is only interested in the energy radiated, the DoF current sources can be mathematically replaced by a much larger number of equivalent sources, that are unphysical, as they are imposed to be uncorrelated at any distance and are distributed all over the volume. The derivation presented here shows explicitly that even the Quantum born, Rytov currents, can be interpreted as mathematically constructed energetically equivalent currents, that have no physical meaning, and whose origin needs to be established.