  Motivated by recent applications of the open quantum system formalism to
understand quarkonium transport in the quark-gluon plasma, we develop a set of
coupled Boltzmann equations for open heavy quark-antiquark pairs and quarkonia.
Our approach keeps track of the correlation between the heavy quark-antiquark
pair from quarkonium dissociation and thus is able to account for both
uncorrelated and correlated recombination. By solving the coupled Boltzmann
equations for current heavy ion collision experiments, we find correlated
recombination is crucial to describe the data of bottomonia nuclear
modification factors. To further test the importance of correlated
recombination in experiments, we propose a new observable:
$\frac{R_{AA}[\chi_b(1P)]}{R_{AA}[\Upsilon(2S)]}$. Future measurements of this
ratio will help distinguish calculations with and without correlated
recombination.
