  A general theory of photon-mediated energy and momentum transfer in N-body
planar systems out of thermal equilibrium is introduced. It is based on the
combination of the scattering theory and the fluctuational-electrodynamics
approach in many-body systems. By making a Landauer-like formulation of the
heat transfer problem, explicit formulas for the energy transmission
coefficients between two distinct slabs as well as the self-coupling
coefficients are derived and expressed in terms of the reflection and
transmission coefficients of the single bodies. We also show how to calculate
local equilibrium temperatures in such systems. An analogous formulation is
introduced to quantify momentum transfer coefficients describing
Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal
equilibrium are readily obtained as a particular case. As an illustration of
this general theoretical framework, we show on three-body systems how the
presence of a fourth slab can impact equilibrium temperatures in heat-transfer
problems and equilibrium positions resulting from the forces acting on the
system.
