2 count separately the number of collision/coalescence (two phonons in, one out; Class 1) and decay/emission pathways (one phonon in, two out; Class 2). It has been noted in previous work that the N 2 can be used to explain the non-smooth variation of the phonon linewidths with respect to frequency and wavevector, with large N 2 tracking broader linewidths and shorter phonon lifetimes. For comparison between systems, it is useful to average the N 2 over q q q to obtain functions of frequency only, i.e.: