We have earlier assumed the existence of a local temperature $T$ and thereby a corresponding spherically symmetric equilibrium distribution, familiar from Bose statistics: $fEq(x,k,T)=fEq(x,k,T)\u2261fEq(T)$. This local temperature is established by some high-capacity reservoir. Equation (2) is the quasi-ballistic mode BTE in the absence of source terms; thus, we assume that no external source of heat couples to the quasi-ballistic modes. We begin with the observation that, owing to the orthogonality of the spherical harmonics [21], the *x*-component of the quasi-ballistic heat flux is determined solely by the first spherical harmonic $g1$Display Formula

(3)$Q(x,t)=2\pi \u2211k\u222b\theta =0\pi \u210f\omega g(x,k,t)v\u2009cos\u2009\theta \u2009sin\u2009\theta d\theta =4\pi 3\u2211k\u210f\omega vg1(x,k,t)$