  Wave propagation and diffusion in linear materials preserve local reciprocity
in terms of a symmetric Green's function. For wave propagations, the relation
between the fields entering and leaving a system is more relevant than the
detailed information about the fields inside it. In such cases, the global
reciprocity of the scattering off a system through several ports is more
important, which is defined as the symmetric transmission between the
scattering channels. When a two-port system supports non-reciprocal
(electromagnetic, acoustic) wave propagation, it is a (optical, phonon) diode
directly following the definition. However, to date no concrete definition or
discussion has been made on the global reciprocity of diffusive processes
through a multiple-port system. It thus remains unclear what are the
differences and relations between the three concepts, namely local
non-reciprocity, global non-reciprocity, and diode effect in diffusion. Here,
we provide theoretical analysis on the frequency-domain Green's function and
define the global reciprocity of heat diffusion through a two-port system,
which has a different setup from that of a thermal diode. We further prove the
equivalence between a heat transfer system with broken steady-state global
reciprocity and a thermal diode, assuming no temperature-dependent heat
generation. The validities of some typical mechanisms in breaking the diffusive
reciprocity and making a thermal diode have been discussed. Our results set a
general background for future studies on symmetric and asymmetric diffusive
processes.
