Hyperdynamics for entropic systems: Time-space compression and pair correlation function approximation

We develop a generalized hyperdynamics method that is able to simulate slow dynamics in atomistic general (both energy- and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body entropy, form a low-dimensional collective space, which is a good approximation that is able to distinguish stable and transitional conformations. A bias potential, which raises the energy in stable regions, is constructed on the fly. We examine the slow nucleation processes of a Lennard-Jones gas and show that our method can generate correct long-time dynamics without prior knowledge.

Figure 1

(Color online) The distribution of transition time of the gas phase in direct MD $(\alpha =1)$ and biased MD $(\alpha =20)$ simulations. The inverse slope of the least-squares fit to the points (solid line) gives the lifetime of the gas phase. $n=0.014$, $N=400$, and $T=0.613$. Inset: the time boost in a typical biased MD simulation is shown.

Figure 2

(Color online) Top: The distributions of two-body entropy $S_2$ from nonbiased and biased simulations. The rebuilt distribution of the bias simulation is also shown. Here, $n=0.008$, $N=1000$, and $T=0.613$. Bottom: The free energy profiles from the nonbiased and biased simulations are compared. The inset shows the simulated samples in the $(S_2,V)$ space. The observed liquid phase does not show here.