A generalized enhanced Fourier law and underlying connections to major frameworks for quasi-ballistic phonon transport

An enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables, is derived from the Boltzmann transport equation, assuming a gray population of quasi-ballistic phonon modes. This equation is generalized to an arbitrary phonon population. Other phonon transport models are analyzed in the context of the generalized EFL and connections are made between the generalized EFL and other models, revealing the essential unity of seemingly disparate models reported in the literature.