  We calculate the dissociation and recombination rates of $\Upsilon(1S)$ in
quark-gluon plasma by using potential non-relativistic QCD. We then study the
dynamical in-medium evolution of the $b\bar{b}-\Upsilon$ system in a periodic
box via the Boltzmann equation and explore how the system reaches equilibrium.
We find that interactions between the free heavy quarks and the medium are
necessary for the system to reach equilibrium. We find that the angular
distribution of $\Upsilon(1S)$ probes the stages at which recombination occurs.
Finally, we study the system under a longitudinal expansion and show that
different initial conditions evolve to distinct final ratios of hidden and open
$b$ flavors. We argue that experimental measurements of the ratio could address
open questions in the quarkonium production in heavy ion collisions.
