4 0 0.5 1 1.5 t$_{w}$=0  ns t$_{w}$=0.33  ns t$_{w}$=16.7  ns -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 S (q,t w ) 0 1 2 3 4 5 6 7 8 q  [Å $^{-1}$] 0 0.1 0.2 0.3 0.4 0.5 0.6 O-O Si-O Si-Si 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 t  [ns] 0 0.2 0.4 0.6 0.8 1 C q (t w ,t w +t) t$_{w}$=24.0  ns q=1.7 Å -1 O t$_{w}$=0  ns FIG. 3: (Color online) Partial structure factors S αβ ( q, t w ) as defined in Eq. (2) for the temperature quench T i = 5000 K to T f = 2500 K. Indicated with arrows are the wave vectors q which have been used to determine C q ( t w , t w + t ) as defined in Eq. (3). FIG. 4: (Color online) C q ( t w , t w + t ) as defined in Eq. (3) for the quench T i = 5000 K to T f = 2500 K for O-atoms and q = 1 . 7 ˚ A $^{$_{−}$1}$. Waiting times for the solid lines are from bottom to top t w = 0 ns, 1 . 63 · 10 $_{−}$4 ns, 1 . 63 · 10 $_{−}$3 ns, 1 . 63 · 10 $_{−}$2 ns, 0 . 33 ns, 0 . 49 ns, 1 . 17 ns, 1 . 96 ns, 8 . 83 ns, 16 . 67 ns, and 23 . 98 ns. The order of solid lines are for increasing t w black thin, green (gray) thin, black thick, green (gray) thick, black thin, green (gray) thin, etc. Error bars are as indicated exemplary. The thick dashed line corresponds to C q ( t w , t w + t ) = F s ( q, t ) at 5000 K. which is a measure for the correlations of the positions at time t$_{w}$ and at a later time ( t$_{w}$ + t ). We investi- gated wave vectors of magnitude q = 1 . 7 , 2 . 7 , 3 . 4 , 4 . 6 , 5 . 5 and 6 . 6 ˚ A − $^{1}$, as indicated with arrows in Fig. 3. We show in Fig. 4 and Figs. 6 - 8 results for the first sharp diffraction peak at q = 1 . 7 ˚ A − $^{1}$. Similar results are found for all other investigated wave vectors. Figure 4 shows C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) for the largest investigated temperature quench from T$_{i}$ = 5000 K to T$_{f}$ = 2500 K for waiting times t$_{w}$ = 0 - 23.98 ns, as listed in the figure caption of Fig. 4. We find that C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) is dependent on t$_{w}$ for all but the last three investigated waiting times. For very short times t ≲ 5 · 10 − 5 ns and zero waiting time, C$_{q}$ ( t$_{w}$ = 0 , t ) is well approximated by C$_{q}$ of the high tem- perature T$_{i}$ = 5000 K from which the system has been quenched (see dashed line in Fig. 4). Thus, C$_{q}$ ( t$_{w}$ = 0 , t ) for very short times is only dependent on T$_{i}$ , q and the particle type, but independent of T$_{f}$ . For times of the order of t = 10 − $^{3}$ns, C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) is oscillatory due to the small system size. For times t ≳ 10 − $^{3}$ns, C$_{q}$ decays to zero without forming a plateau for small t$_{w}$ . With increasing t$_{w}$ a plateau is formed, which is independent of t$_{w}$ for t$_{w}$ ≥ 0 . 33 ns. To characterize the plateau height we define F as the time average of C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) for times 2 . 55 ps ≤ t ≤ 6 . 64 ps. The inset of Fig. 5 shows that for large waiting times F ( t$_{w}$ ) becomes independent of t$_{w}$ and of T$_{i}$ . To test this independence of T$_{i}$ further, we show F as a function of q for t$_{w}$ = 16 . 67 ns in Fig. 5. We find that the plateau height is dependent on the particle type and decreases with decreasing q , but F is independent of T$_{i}$ . The plateau in C$_{q}$ becomes more horizontal with de- creasing final temperature T$_{f}$ , as can be seen by the com- parison of Fig. 4 ( T$_{f}$ = 2500 K) and Fig. 6 ( T$_{f}$ = 3000 K). Times t ≳ 0 . 1 ns correspond to the α -relaxation, where C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) decays from the plateau to zero. For the quench from 5000 K to 2500 K (see Fig. 4) this decay depends on t$_{w}$ for all t$_{w}$ < 8 . 83 ns. However, for t$_{w}$ ≥ 8 . 83 ns (the largest three t$_{w}$ ), C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) is independent of t$_{w}$ not only for intermediate times t (plateau) but for all times (including the α -relaxation). Thus, the system reaches equilibrium during the simulation run. For the quench from 3760 K to 3000 K (see Fig. 6), C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) becomes independent of t$_{w}$ for t$_{w}$ ≳ 1 ns, which means that the time at which equilibrium is reached is depen- dent on the temperature quench. To estimate the time when the system reaches equilib- rium for each ( T$_{i}$, T$_{f}$ ) combination, we next quantify the decay of C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) . Instead of taking a vertical cut in C$_{q}$ ( t$_{w}$, t$_{w}$ + t ) as we did for F , we now take a hori- zontal cut. We define the decay time t Cq r to be the time t = t Cq r for which C$_{q}$ ( t$_{w}$, t$_{w}$ + t Cq r ) = C$_{cut}$ . We chose C$_{cut}$ = 0 . 625 / 0 . 41 / 0 . 295 / 0 . 155 / 0 . 085 / 0 . 04) for the Si particles and C$_{cut}$ = 0 . 625 / 0 . 305 / 0 . 195 / 0 . 08 / 0 . 04 / 0 . 014 for the O particles at the wavenumbers q = 1 . 7 / 2 . 7 / 3 . 4 / 4 . 6 / 5 . 5 / 6 . 6 ˚ A − $^{1}$, respectively. The resulting decay times t Cq r as a function of waiting time t$_{w}$ are shown in Fig. 7a for O-atoms and in Fig. 7b for Si-atoms. Color (black or green/gray) indicates the initial temperature T$_{i}$