Scattering approach to Casimir forces and radiative heat transfer for nanostructured surfaces out of thermal equilibrium

We develop an exact method for computing Casimir forces and the power of radiative heat transfer between two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of the intervening surfaces.