In previous works (ijsciences1, ijsciences2), we considered that the q-Gaussians can be used to represent the stochastic Kubo lineshapes, which are characterized by the time scale of fluctuations. As discussed by Tokmakoff, "a fluctuating environment influences measurements of an experimentally observed internal variable". Tokmakoff explains that, "in condensed matter, time-dependent interactions with the surroundings can lead to time-dependent frequency shifts, known as spectral diffusion. How these dynamics influence the line width and lineshape of absorption features depends on the distribution of frequencies available to your system Δ and the time scale of sampling varying environments (𝜏 𝑐 )" . There are three cases of line broadening. We have the homogeneous and the inhomogeneous broadening, and a more general case of "spectral diffusion", with the system positioned between the homogeneous and inhomogeneous cases (see Tokmakoff for explanation). For what is regarding the resulting lineshape according to stochastic theory of fluctuation, in Kubo approach, a discussion is available in LibreTexts-Chemistry. The homogeneous broadening is giving a lineshape which is close to a Lorentzian profile, whereas the homogeneous case is like a Gaussian profile, with differences in the far wing region, as we have shown in ijsciences1, ijsciences2.