Non-reciprocity and heat transfer in far from equilibrium processes

A non-reciprocal phonon model for microwave or optical isolators is considered. It gives a simpler framework to further investigate the formerly argued possibility for a heat transfer between black bodies at common temperatures. While the non-dissipative device retains the Detailed Balance property, the presence of dissipation breaks it. This property allows a net transfer of heat between the two black bodies at common temperatures, whenever the absorptive elements are at lower temperatures than the one being common to the bodies.