Thermodynamic equivalence of cyclic shear and deep cooling in glass formers

The extreme slowing down associated with glass formation in experiments and in simulations results in serious difficulties to prepare deeply quenched, well annealed, glassy material. Recently, methods to achieve such deep quenching were proposed, including vapor deposition on the experimental side and “swap Monte Carlo” and oscillatory shearing on the simulation side. The relation between the resulting glasses under different protocols remains unclear. Here we show that oscillatory shear and swap Monte Carlo result in thermodynamically equivalent glasses sharing the same statistical mechanics and similar mechanical responses under external strain.

Figure 1

Average energy per particle in a binary system with $N=1024$ as a function of the inverse density after cooling at six different rates, three using regular Monte Carlo and three swap Monte Carlo. The best fit has a slope of $2.24\pm 0.01$ in perfect agreement with the equation of state. Eq. (5). Note that Eq. (5) is valid only on the average. To underline this, typical fluctuations in energy and density leading to the lowest average energy in this graph are shown in blue.

Figure 2

Average energy per particle in a binary system with $N=1024$ as a function of the inverse density after $1,2...,6$ cycles of quasistatic shear strain with ${\gamma }_{\max }=0.04$. The same equation of state, Eq. (5), is obeyed.

Figure 3

Average energy per particle in a polydispersed system with $N=1024$ as a function of the inverse density after cooling at seven different rates, three using regular Monte Carlo and four swap Monte Carlo. The best fit has a slope of $2.250\pm 0.005$ in perfect agreement with the equation of state, Eq. (5).

Figure 4

Average energy per particle in a polydispersed system with $N=400$ [panel (a)] and $N=625$ [panel (b)] as a function of the inverse density after 24 and 10 cycles, respectively, of quasistatic shear strain with ${\gamma }_{\max }=0.04$. The same equation of state, Eq. (5), is obeyed with the slopes $2.25\pm 0.01$ and $2.23\pm 0.02$, respectively.

Figure 5

Probability distribution functions (pdfs) for the total energy per particle in the binary and polydispersed examples [panels (a) and (b), respectively). In both cases the results pertain to $N=400$.

Figure 6

Athermal quasistatic stress vs strain averaged over 30 of polydispersed configuration. Here $N=400$ and the configurations were taken from an ensemble whose average energy is $\langle U\rangle /N=1.96$.

Figure 7

An example of the effect of cyclic shear on the average virial of a binary system with Lennard-Jones interaction at $T=0.1$. The protocol is the same as in Fig. 2. $\epsilon$ and ${\sigma }_{ab}$ are the same as in the binary systems with inverse power-law potential. The agreement with Eq. (10) is apparent, indicating that as the system compactifies it does not fall out of equilibrium.