Emergence of Nonlocal Hydrodynamics in Many-Body Radiative Heat Transport

We develop a nonlocal hydrodynamic theory of radiative heat transport in many-body systems by coarse graining their microscopic electrodynamic interactions. Long-range radiative exchange naturally generates a spatially nonlocal constitutive relation in which the heat current at a given position depends on temperature gradients over an extended region, while energy conservation retains its local conservative form. Fourier transport emerges as a controlled long-wavelength limit when the interaction kernel has a finite second spatial moment. When this moment fails to converge, spatial nonlocality survives coarse graining and gives rise to non-Fourier transport. The resulting framework establishes a systematic bridge between discrete many-body fluctuational electrodynamics and a continuous description of radiative heat transport.