Fundamental limits for non-contact transfers between two bodies

We investigate energy and momentum non-contact exchanges between two arbitrary flat media separated by a gap. This problem is revisited as a transmission problem of individual system eigenmodes weighted by a transmission probability obtained either from fluctuational electrodynamics or quantum field theory. An upper limit for energy and momentum flux is derived using a general variational approach. The corresponding optimal reflectivity coefficients are given both for identical and different media in interaction.