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In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithmwas developed for tracing out a geodesic curve on the constant-potential-energyhypersurface. Here simulations of this NVU dynamics are compared to results forfour other dynamics, both deterministic and stochastic. First, NVU dynamics iscompared to the standard energy-conserving Newtonian NVE dynamics bysimulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version(i.e., with cut-off's at the pair potential minima), and the GaussianLennard-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 presentedfor the equivalence of NVU and NVE dynamics in the thermodynamic limit; inparticular to leading order in 1/N these two dynamics give identicaltime-autocorrelation functions. In the final section NVU dynamics is comparedto Monte Carlo dynamics, to a diffusive dynamics of small-step random walks onthe constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. Iftime is scaled for the two stochastic dynamics to make their single-particlediffusion constants identical to those of NVE dynamics, the simulations showthat all five dynamics are equivalent at low temperatures except at shorttimes.

NVU dynamics. II. Comparing to four other dynamics