\in \mathbb{R}$, so that we have $${\label{eq:mac1}}
    \ddot\alpha(t) + a \dot\alpha(t) + b^2 \alpha(t) = f,$$ which is a differential equation for a damped harmonic oscillator, subject to an externally applied macroscopic force $f$. Furthermore, its solution for $\alpha(t)$ converges with time to the steady-state ensemble average of [Eq. (\[eq:lgv1\])]{}, e.g. [@PRE2016III], with ${\langle\alpha(t)\rangle} = f/b^2$ and ${\langle\dot\alpha(t)\rangle} = 0$. By comparing Eqs. (\[eq:lgv1\]) and (\[eq:mac1\]), one can see that, at the mesoscopic scales, $r(t)$ represents the external force, $f = {\langler(t)\rangle}$, as well as its spontaneous variations [@OM1953].

In the equilibrium regime [@Nyquist1928; @OM1953; @PRE2016II], $f=0$, the stochastic term $r(t)$ represents effects of the thermal fluctuations and is commonly given by $r(t) = A \omega(t)$, where $A > 0$ is a constant proportional to the square root of the system’s temperature, while $\omega(t)$ is a Gaussian white noise with zero mean and unit variance parameters. In general, this model yields a dynamics, which is accurate up to the third-order statistics, due to symmetry considerations [@PRE2016II; @PRE2016III].

Experiments and molecular dynamics simulations, e.g. Refs. [@PRE2016; @PRE2016II], provide an evidence that, besides the thermal fluctuations, an additional source of spontaneous variations, $\epsilon$, is present in the nonequilibrium (NE) regime, $f\ne0$, $${\label{eq:rNE}}r^\mathrm{NE}(t) 