  In chains of closely-spaced nanoparticles supporting surface polaritons,
near-field electromagnetic coupling leads to collective effects and
super-Planckian thermal radiation exchange. Researchers have primarily used two
analytical approaches to calculate radiative heat transfer in these systems:
fluctuational electrodynamics, which directly incorporates fluctuating thermal
currents into Maxwell's equations, and a kinetic approach where the dispersion
relation provides modes and propagation lengths for the Boltzmann transport
equation. Here, we compare results from the two approaches in order to identify
regimes in which kinetic theory is valid and to explain differing results in
the literature on its validity. Using both methods, we calculate the diffusive
radiative thermal conductivity of nanoparticle chains. We show that kinetic
theory is valid and matches predictions by fluctuational electrodynamics when
the propagation lengths are greater than the particle spacing.
