  The equilibria formed by the self-gravitating, collisionless collapse of
simple initial conditions have been investigated for decades. We present the
results of our attempts to describe the equilibria formed in $N$-body
simulations using thermodynamically-motivated models. Previous work has
suggested that it is possible to define distribution functions for such systems
that describe maximum entropy states. These distribution functions are used to
create radial density and velocity distributions for comparison to those from
simulations. A wide variety of $N$-body code conditions are used to reduce the
chance that results are biased by numerical issues. We find that a subset of
initial conditions studied lead to equilibria that can be accurately described
by these models, and that direct calculation of the entropy shows maximum
values being achieved.
