NVU dynamics. II. Comparing to four other dynamics

TL;DR

This paper compares NVU dynamics with four other dynamics types, demonstrating their equivalence in results and behavior in the thermodynamic limit and under certain conditions, especially at low temperatures.

Contribution

It provides the first comprehensive comparison of NVU dynamics with multiple deterministic and stochastic methods, establishing their equivalence in key physical quantities.

Findings

NVU and NVE dynamics produce identical results for key physical quantities.

NVU and NVE dynamics are equivalent in the thermodynamic limit.

All five dynamics are similar at low temperatures when scaled appropriately.

Abstract

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Gaussian Lennard-Jones liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are then presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final section NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.