  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.
