  We study the radiative heat transfer and the Casimir-Lifshitz force occurring
between two bodies in a system out of thermal equilibrium. We consider bodies
of arbitrary shape and dielectric properties, held at two different
temperatures, and immersed in a environmental radiation at a third different
temperature. We derive explicit closed-form analytic expressions for the
correlations of the electromagnetic field, and for the heat transfer and
Casimir-Lifshitz force, in terms of the bodies scattering matrices. We then
consider some particular cases which we investigate in detail: the atom-surface
and the slab-slab configurations.
