Nonlocal theory of thermal conductivity

We have derived a nonlocal theory of thermal conductivity for the case in which the heat is carried by phonons. There is a nonlocal relation between the heat current J(r) and the temperature gradient {∇}T(r'). The nonlocal theory is needed whenever the phonon mean free path is long compared to the distance scale of the variation in {∇}T. The theory is used to explain some previous experiments in silicon.