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In this work we show that Non-equilibrium Greens Function Perturbation Theory (NEGF) is really the overarching perturbative transport theory. It is developed in 3 directions: Landauer-like theory, kinetic theory and Green-Kubo linear response theory. This work generalizes the 2 directions of Landauer-like theory and the kinetic theory. Firstly, NEGF is used to derive phonon-phonon Hedin-like functional derivative equations which generates conserving self energy approximations for phonon-phonon interaction. Secondly, for the Landauer-like theory, using the perturbation expansion, we obtain...