  We study the constraints on reciprocal and non-reciprocal many-body radiative
heat transfer imposed by symmetry and the second law of thermodynamics. We show
that the symmetry of such a many-body system in general forms a magnetic group,
and the constraints of the magnetic group on the heat transfer can be derived
using a generalized reciprocity theorem. We also show that the second law of
thermodynamics provides additional constraints in the form of a nodal
conservation law of heat flow at equilibrium. As an application, we provide a
systematic approach to determine the existence of persistent heat current in
arbitrary many-body systems.
