  Traditional theories of interfacial heat transfer by atomic vibrations, also
known as phonons, do not explain how vibrational mode interactions contribute
to interface conductance. Traditional methods also use the concept of phonons
as particles or waves which propagate and transmit energy through interfaces;
such methods are therefore inapplicable to realistic non-crystalline systems
where phonons are not propagating. Here we introduce a more general formalism
of interfacial phonon transport, rigorously derived from interatomic
interactions projected onto the normal modes of the system, showing for the
first time how interactions between vibrational modes contribute to thermal
interface conductance. This new physical picture is based on the concept of
forces and energy exchange between modes, regardless of their propagating or
non-propagating character, thus providing a general formalism to describe
phonon transport in all solids regardless of disorder.
