  This paper is the second in a series investigating the evolution of star
clusters towards energy equipartition (EEP). Here, we focus on the effects of
the external tidal field of the host galaxy, initial anisotropy in the velocity
distribution, and primordial binary star population. The results of our
$N$-body simulations show that regardless of the strength of the tidal field or
the fraction of primordial binaries: (i) the evolution towards EEP in the
intermediate and outer regions of initially anisotropic systems is more rapid
than for isotropic systems; (ii) this evolution also proceeds at different
rates for the tangential and radial components of the velocity dispersion; and
(iii) the outer regions of the initially isotropic systems show a tendency to
evolve towards a state of `inverted' EEP in which low-mass stars have smaller
velocity dispersion than high-mass stars. We also find that the clusters with
primordial binaries stay even farther from EEP than systems containing only
single stars. Finally, we show that all these results also hold when the degree
of EEP is calculated using quantities measured in projection as it is done in
observational studies, and that our findings could be tested with current and
upcoming observational data.
