$\dot\alpha(t)$.

In addition, Appendix \[sec:apx\] reveals a mathematical analogy between the models of athermal noise, considered here. In particular, they can be regarded as Padé approximants for certain generating functions of the exact probability distribution, associated with $\epsilon(t/\tau)$. The mathematical structure, described in Appendix \[sec:apx\], is applicable also to other families of approximations. This, in principle, allows formulation of alternative models for athermal noise.

Finally, for simulations of the Langevin dynamics, Appendix \[sec:alg\] proposes an algorithm, which is used to integrate [Eq. (\[eq:lgv2\])]{} in [Sec. \[sec:mes\]]{}. Our numerical scheme minimizes sampling of random variables, which is usually a most intensive part of the computations. In this regard, the Langevin equation with simple exponential noise has an advantage over exponential shot noise, because it requires only one random number generation per step of numerical integration; cf. Appendix \[sec:alg\]. In the macroscopic limit our simulation method coincides with a second-order symplectic algorithm, which respects the time reversibility of [Eq. (\[eq:mac1\])]{}.

\[sec:mic\]Molecular Dynamics Simulations
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![\[fig:kfig\] Plot of the athermal cumulant ratio, $k(P_{yx})$, as a function of the shear rate, $\gamma$, for our MD simulations. Error bars are given by one standard deviation. A nearly linear trend can be fit to a line, 