  We examine the medium time quantum dynamics and population equilibration of
two, three and four-well Bose-Hubbard models using stochastic integration in
the truncated Wigner phase-space representation. We find that all three systems
will enter at least a temporary state of equilibrium, with the details
depending on both the classical initial conditions and the initial quantum
statistics. We find that classical integrability is not necessarily a good
guide as to whether equilibration will occur. We construct an effective
single-particle reduced density matrix for each of the systems, using the
expectation values of operator moments, and use this to calculate an effective
entropy. Knowing the expected maximum values of this entropy for each system,
we are able to quantify the different approaches to equilibrium.
