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We study the constraints on reciprocal and non-reciprocal many-body radiativeheat transfer imposed by symmetry and the second law of thermodynamics. We showthat 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 derivedusing a generalized reciprocity theorem. We also show that the second law ofthermodynamics provides additional constraints in the form of a nodalconservation law of heat flow at equilibrium. As an application, we provide asystematic approach to determine the existence of persistent heat current inarbitrary many-body systems.

Theoretical constraints on reciprocal and non-reciprocal many-body radiative heat transfer