parameter $F$ is essential in [Eq. (\[eq:lgv2\])]{}. In particular, it allows our Langevin model for $P_{yx}$ to achieve the statistical accuracy of third order. Consider the following quantity, which relates the first three cumulants of $P_{yx}$, $$k(P_{yx}) = \frac{\chi^2(P_{yx})}{\kappa_1(P_{yx}) \kappa_3(P_{yx})},$$ Below we refer to $k(P_{yx})$ as [*the athermal cumulant ratio*]{}, because it captures effects of the athermal noise in [Eq. (\[eq:lgv2\])]{} and vanishes in equilibrium systems together with $\chi(P_{yx})$; cf. [Eq. (\[eq:eqkappa2\])]{}.

As can be deduced from Eqs. (\[eq:kappaex\]) and (\[eq:kappash\]), the athermal cumulant ratio, for both models of athermal noise considered in [Eq. (\[eq:lgv2\])]{}, has a general form $${\label{eq:kform}}
    k \propto ({\mathrm{const}}_1 F \tau / B + {\mathrm{const}}_2)^{-1}{,}$$ where ${\mathrm{const}}_1$ and ${\mathrm{const}}_2$ are some constants, which do not depend on the shear rate. By substituting $F=0$ into [Eq. (\[eq:kform\])]{}, we see, that without a force term $F$ on the right-hand side of [Eq. (\[eq:lgv2\])]{} in both cases, simple exponential noise and exponential shot noise, $k$ would be independent of $\gamma$.

We plot $k(P_{yx})$ as a function of $\gamma$ for our MD simulations in [Fig. \[fig:kfig\]]{}, where a nearly linear trend can be observed. In particular, this implies, that $\chi(P_{yx})$, which essentially expresses the athermal variance of $P_{yx}$, vanishes faster 