Trace formulas for nonequilibrium Casimir interactions, heat radiation, and heat transfer for arbitrary objects

We present a detailed derivation of heat radiation, heat transfer, and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The results can be expressed as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that is not due to radiation pressure.