Figure 1

(a) Temperature protocol in the Kovacs experiment: the system equilibrated at $T_h$ is quenched at several $T_l$ (1) where it relaxes for a time $t_e$ (2). It is finally heated at $T$ (3). (b) Corresponding volume evolution in the cases of low (A) and high (B) $T_l$. (c) Volume relaxation for the OTP model at different $T_l$. The fast relaxation taking place on times shorter than the thermostat characteristic time is not reported.Reuse & Permissions

Figure 2

Volume relaxation showing the crossover effect in a molecular system. (a) A system of 343 OTP molecules at constant $P=16\mathrm{M}\mathrm{P}\mathrm{a}$ is equilibrated at $T_h=400\mathrm{K}$, quenched at several low temperatures $T_l$ and left to age for $t_e=50\mathrm{n}\mathrm{s}$, a time insufficient to reach equilibrium at $T_l$. The system is then heated at the intermediate temperature $T=280\mathrm{K}$ and the $V$ relaxation dynamics is recorded (symbols). For the case $T_l=T$, the system is directly brought from $T_h=400\mathrm{K}$ to $T=280\mathrm{K}$ and hence $t_e=0$. The vertical dashed lines indicate the transient time, where $T$ and $P$ have not yet equilibrated to the final values. (b) Volume relaxation at $T=280\mathrm{K}$, at fixed $T_l=150\mathrm{K}$ for different $t_e$ values. Dashed lines delimit the transient region, when neither $T$ nor $P$ have reached their equilibrium value.Reuse & Permissions

Figure 3

Kovacs effect for $T_l=150\mathrm{K}$ and $t_e=25\mathrm{n}\mathrm{s}$; average over 200 independent realizations. The out-of-equilibrium evolutions of (a) system volume $V$, (b) inherent structures $e_{\mathrm{I}\mathrm{S}}$, (c) inherent structure pressure $P_{\mathrm{I}\mathrm{S}}$, and (d) shape factor $\mathcal{S}$ are shown. Error bars are smaller than the symbols. Two points (labeled $P_{<}$ and $P_{<}$), characterized by the same values of $T$, $P$, and $V$, are marked by arrows.Reuse & Permissions

Figure 4

Landscape relations $e_{\mathrm{I}\mathrm{S}}(V)$, $P_{\mathrm{I}\mathrm{S}}(V)$, and $\mathcal{S}(V)$ along the constant $P_{\mathrm{I}\mathrm{S}}=-225.8\mathrm{M}\mathrm{P}\mathrm{a}$ path. Equilibrium data (solid lines) are generated from the analysis of equilibrium simulations at different state points but at constant $P_{\mathrm{I}\mathrm{S}}$. Symbols refer to the relaxation dynamics at $T=280\mathrm{K}$, for samples which have aged at $T_l=150$, 220, and 280 K. Only data for times longer than 20 ps—the time associated with the establishment of constant $T$ and $P$ conditions—are shown. The vertical arrows indicate $P_{<}$ and $P_{>}$ (see Fig. 3).Reuse & Permissions