(a) Phase diagram of the soft-core system. Data for the liquid (and quenched glass) branch (red open squares) and for the crystal (fcc) branch (black filled circles) are shown. The blue circles are the points for the metastable states that were obtained in our previous work 5 after NVE relaxations. The dotted blue curve shows the glass branch that represents these points. The position of ρ p * (= T p*−0.25) is also shown in the diagram. The data points obtained from rapid cooling (run 1) are connected by the dashed red curve. An example of the trajectory of for NVE relaxation is shown by the solid purple curve on the diagram. (b) Pair correlation functions, g(r), for several points ((a), (b), and (c), shown in (a)) on the phase diagram.
(a) U*/N values for rapid cooling along the liquid branch (red open squares) that is shown in the phase diagram in Fig. 1 . The values for the glass branch (blue circles) and for the crystal (fcc) branch (black filled circles) are also shown. The values for the rapid heating process (pink filled triangles) are also plotted. (b) The plot on an enlarged scale for the rapid cooling case shown in (a).
(a) The C V curves along the rapid quenching (run 1), obtained from polynomial fitting using Eqs. (16) and (17) for < T*(red solid curve) ( ∼ 0.31) and using Eqs. (23) and (25) for T* < (red dashed curve). The C P values for < T* (pink solid curve) and for T* < (pink dashed curve) calculated from Eq. (15) are also shown. The C V values (blue dotted curve) and C P values (purple dotted curve) for the crystalline states (fcc) (Ref. 6 ) are shown for comparison. (b) Similar plots as in (a) versus lnT*. (c) C V obtained from the fluctuation of the kinetic energy using Eq. (30) along the rapid quenching of a liquid. Red circles: the C V values obtained using an averaging time of 100 ps (for argon) in the liquid state. Blue filled squares: the C V values obtained using an averaging time of 20 ps (for argon) before NVE relaxation. The values for the short time scale change more rapidly. Black squares: The values along the glass branch, in which an averaging time longer than 1 ns was used.
(a) Entropy curves obtained along the rapid quenching liquid (glass) plotted against T*. The same color as in Fig. 3(a) is used. (b) Entropy curves obtained along the rapid quenching liquid (glass) plotted against lnT*. (c) The anharmonic contribution of the excess entropy, ΔSah, obtained using Eq. (31) (green solid curve). The logarithmic term was omitted because C1ql (the C1 value for the quenched liquid (glass)) is comparable to C1cryst (the C1 value for the fcc crystal). The contribution of the residual entropy was also omitted. The ΔSah value appears to converge to 0 in the T*∼ 0 limit.
Specific heat C V obtained from the fluctuation of the kinetic energy by Eq. (30) along the NVE relaxation (ρ0* = 1.48) as a function of time. The values are calculated using three fixed averaging times. The data intervals used are 100 time steps (1 step = 1 fs for argon). Blue: the averaging of every 10 000 points. Purple: the averaging of every 20 000 points. Red: the averaging of every 30 000 points. The relaxation curve (light green) for g t * is shown in comparison. The curve of the time-dependent C V shows a peak in the middle region, and its height depends on the averaging time.
(a) Changes in g* and in T* along an NVE non-equilibrium relaxation during a 600 000-step run that starts from = 1.36 and g* = 30.75. (b) Changes in the probability distribution of , p(T*), during the run. The distribution in each 100 000-step time region (dt = 4.7 × 104) are shown from left to right. The distribution was normalized to 1 in each region. A change in the distribution occurs gradually but with discrete levels of states.
Typical MTM spectra for (a) the liquid at T* = 0.52 and (b) the crystal (fcc) at T* = 0.35. Both spectra were obtained from the time series of T t* that is related to C V for the run with 100 000 steps. In the reshaped spectrum (red), the contribution of harmonic signals (black) was removed.
MTM spectra for the time series of during and after NVE relaxation. (a) = 0.355 for the 100 000-step run after beginning relaxation. (b) After relaxation (500 000-600 000 steps) of the run in (a).
The values g* that are used for the calculation of C V along the rapid cooling of the system (run 1). U*/N values are also shown for the low T* region. The values for ρ* < 1.3 are for the equilibrated states. The values for ρ* ∼ 1.36 are for the quasi-equilibrated state before non-equilibrium relaxation. The values forρ* > ∼1.4 are for the trapped states.
Coefficients, B n, obtained for the liquid and rapidly quenched liquid states using Eq. (16) . The C V values were calculated for T* > 0.33 using these coefficients. The relation between the observed g * values and the ones calculated using the coefficients is shown in the last row with the goodness of fit for the region 0.33 < T* < 1.58.
Results of the C n coefficients for rapidly quenched liquids, including the non-equilibrium and trapped states (run 1). The C V values were obtained from these coefficients using Eq. (25) . The relation between the observed U*/N values and the ones calculated using the coefficients is shown in the last row with the goodness of fit for the region 0.0017 < T* < 0.38.
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