exponential noise and white exponential shot noise, were compared in [Sec. \[sec:mes\]]{}. Within the third-order statistics they provide equivalent results. As explained in Appendix \[sec:apx\], these two models belong to two, among many other, possible families of approximants for certain generating functions of the true probability distribution, associated with athermal noise $\epsilon(t)$. Therefore, from the statistical and mathematical perspectives, they are equivalent and interchangeable. The difference of the physical interpretations between the considered models of athermal noise, which might have distinct consequences for the first-order Langevin dynamics [@MO1953; @PRE2016II], in the second-order equation (\[eq:lgv2\]) applies mostly to $\dot\alpha(t)$, and does not affect significantly the behavior of $\alpha(t)$.

The above models of athermal noise differ by their values of the fourth cumulant. Within the statistical uncertainties of the original system considered in [Sec. \[sec:mic\]]{}, this discrepancy is, however, completely negligible; cf [Sec. \[sec:mes\]]{}. Statistically the excess kurtosis of our MD and LD data for $\alpha(t)$ is comparable to that of a Gaussian probability distribution, which equals zero.

To characterize the third-order statistics of athermal noise, we introduced a new quantity, [*athermal cumulant ratio*]{}, which has a nearly linear dependence on the external shear rate. This observation was analyzed in [Sec. \[sec:mic\]]{}, 