Statistical mechanics of collisionless orbits. III. Comparison with
  N-body simulations
  We compare the DARKexp differential energy distribution, N(E) \propto
\exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the
results of N-body simulations of dark matter halos. We first demonstrate that
if DARKexp halos had anisotropic velocity distributions similar to those of
N-body simulated halos, their density and energy distributions could not be
distinguished from those of isotropic DARKexp halos. We next carry out the
comparison in two ways, using (1) the actual energy distribution extracted from
simulations, and (2) N-body fitting formula for the density distribution as
well as N(E) computed from the density using the isotropic Eddington formula.
Both the methods independently agree that DARKexp N(E) with \phi_0\approx 4-5
is an excellent match to N-body N(E). Our results suggest (but do not prove)
that statistical mechanical principles of maximum entropy can be used to
explain the equilibrated final product of N-body simulations.
