noise, [Eq. (\[eq:kappar\])]{} thus yields: $$\begin{aligned}
{\label{eq:kappaex}}
    \kappa_1(\alpha) &=& \frac{F_\mathrm{ex} + B_\mathrm{ex}/\tau_\mathrm{ex}}{b^2};\quad
    \kappa_2(\alpha) = \frac{A^2 + B_\mathrm{ex}^2/\tau_\mathrm{ex}}{2 a b^2};\nonumber\\
    \kappa_3(\alpha) &=& \frac{4 B_\mathrm{ex}^3}{3 b^2 (2 a^2 + b^2) \tau_\mathrm{ex}}.\end{aligned}$$ And similarly, for exponential shot noise, we get $$\begin{aligned}
{\label{eq:kappash}}
    \kappa_1(\alpha) &=& \frac{F_\mathrm{sh} + B_\mathrm{sh}/\tau_\mathrm{sh}}{b^2};\quad
    \kappa_2(\alpha) = \frac{A^2 + 2 B_\mathrm{sh}^2/\tau_\mathrm{sh}}{2 a b^2};\nonumber\\
    \kappa_3(\alpha) &=& \frac{4 B_\mathrm{sh}^3}{b^2 (2 a^2 + b^2) \tau_\mathrm{sh}}.\end{aligned}$$ cf. [@PRE2016II; @PRE2016III]. The constants $A$, $a$ and $b$ do not depend on the shear rate, and we also have $${\label{eq:eqkappa2}} \kappa_2(\alpha|\gamma=0) = \frac{A^2}{2 a b^2};$$ cf. [Sec. \[sec:intro\]]{}. Equations (\[eq:kappaex\])-(\[eq:eqkappa2\]) suggest then to define a nonequilibrium part of the second cumulant as $$\chi(\alpha) = \kappa_2(\alpha) - \frac{A^2}{2 a b^2}.$$

![image](trj){width="2\columnwidth"}

Formulas (\[eq:kappaex\]) and (\[eq:kappash\]) form a system of equations, which can be solved for the parameters of [Eq. (\[eq:lgv2\])]{}, $$\begin{aligned}
{\label{eq:kappas}}
    B_\mathrm{ex} &=& \frac{3 (2 a^2 + b^2) \kappa_3(\alpha)}{8 a \chi(\alpha)} = 3 B_\mathrm{sh} / 2;
    \nonumber\\
    \tau_\mathrm{ex} &=& \frac{9 (2 a^2 + b^2)^2 \kappa_3^2(\alpha)}{128 a^3 b^2 \chi^3(\alpha)} = 9 \tau_\mathrm{sh} / 8;\end{aligned}$$ whereas $F$ is calculated by the residual principle, $F = b^2\kappa_1(\alpha) - B/\tau$, with $B$ and $\tau$ being the parameters of the chosen athermal noise model.

In [Sec. \[sec:intro\]]{} we promised to show, that the 