  We present a general nonequilibrium Green's function formalism for modeling
heat transfer in systems characterized by linear response that establishes the
formal algebraic relationships between phonon and radiative conduction, and
reveals how upper bounds for the former can also be applied to the latter. We
also propose an extension of this formalism to treat systems susceptible to the
interplay of conductive and radiative heat transfer, which becomes relevant in
atomic systems and at nanometric and smaller separations where theoretical
descriptions which treat each phenomenon separately may be insufficient. We
illustrate the need for such coupled descriptions by providing predictions for
a low-dimensional system of carbyne wires in which the total heat transfer can
differ from the sum of its radiative and conductive contributions. Our
framework has ramifications for understanding heat transfer between large
bodies that may approach direct contact with each other or that may be coupled
by atomic, molecular, or interfacial film junctions.
