  We present an approach to describing fluctuational electrodynamic (FED)
interactions, particularly van der Waals (vdW) interactions as well as
radiative heat transfer (RHT), between material bodies of vastly different
length scales, allowing for going between atomistic and continuum treatments of
the response of each of these bodies as desired. Any local continuum
description of electromagnetic (EM) response is compatible with our approach,
while atomistic descriptions in our approach are based on effective electronic
and nuclear oscillator degrees of freedom, encapsulating dissipation,
short-range electronic correlations, and collective nuclear vibrations
(phonons). While our previous works using this approach have focused on
presenting novel results, this work focuses on the derivations underlying these
methods. First, we show how the distinction between "atomic" and "macroscopic"
bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and
RHT look very similar regardless of how the distinction is drawn. Next, we
demonstrate that the atomistic description of material response in our approach
yields EM interaction matrix elements which are expressed in terms of
analytical formulas for compact bodies or semianalytical formulas based on
Ewald summation for periodic media; we use this to compute vdW interaction free
energies as well as RHT powers among small biological molecules in the presence
of a metallic plate as well as between parallel graphene sheets in vacuum,
showing strong deviations from conventional macroscopic theories due to the
confluence of geometry, phonons, and EM retardation effects. Finally, we
propose formulas for efficient computation of FED interactions among material
bodies in which those that are treated atomistically as well as those treated
through continuum methods may have arbitrary shapes, extending previous
surface-integral techniques.
