  We propose an extension to the original result derived by Simoncelli et al.
(https://doi.org/10.1038/s41567-019-0520-x) to encompass the effects of a space
and time dependent heat source. Via a Fourier Transfrom, we obtain closed form
expressions for the dynamics of the phonon population and coherence as a
function of heat source.

Mesoscale and Nanoscale Physics