volume of the MD simulation cell, while, for the $i$-th particle, $p_{yi}$, $p_{xi}$, $y_i$, and $F_{xi}$ are, respectively, the $x$ and $y$ components of [*peculiar*]{} linear momentum, $y$-coordinate, and $x$-component of the force due to interactions with the other particles.

Data and results of our simulations are reported in the reduced units (r.u.), described in [@PRE2016III Appendix C]. Here we are interested in a nonequilibrium Langevin equation (\[eq:lgv2\]) for $\alpha(t) = P_{yx}$ accurate up to the third-order moment, which is most reliably estimated for the steady-state probability distribution of $P_{yx}$ observed in systems of a small size; cf. [Ref. [@PRE2016]]{}. Therefore, we conduct our simulations for $N=125$ particles, although at the same number density $0.8$ r.u. and temperature $1$ r.u., as in [Ref. [@PRE2016III]]{}.

As shown in [Ref. [@PRE2016III]]{}, the constants $a$ and $b$ in [Eq. (\[eq:lgv2\])]{} do not depend on $\gamma$ and can be estimated from measurements of the time autocorrelation function of $P_{yx}$. Also, since the temperature is fixed in our simulations by the NH thermostat, the parameter $A$ can be determined from the variance for $P_{yx}$, measured in the equilibrium simulations, i.e. $\kappa_2(P_{yx}|\gamma=0)$; cf. [Sec. \[sec:intro\]]{}. Hence in this section we are mainly concerned with the remaining 