  We use the open quantum system formalism to study the dynamical in-medium
evolution of quarkonium. The system of quarkonium is described by potential
non-relativistic QCD while the environment is a weakly coupled quark-gluon
plasma in local thermal equilibrium below the melting temperature of the
quarkonium. Under the Markovian approximation, it is shown that the Lindblad
equation leads to a Boltzmann transport equation if a Wigner transform is
applied to the system density matrix. Our derivation illuminates how the
microscopic time-reversibility of QCD is consistent with the time-irreversible
in-medium evolution of quarkonium states. Static screening, dissociation and
recombination of quarkonium are treated in the same theoretical framework. In
addition, quarkonium annihilation is included in a similar way, although the
effect is negligible for the phenomenology of the current heavy ion collision
experiments. The methods used here can be extended to study quarkonium
dynamical evolution inside a strongly coupled QGP, a hot medium out of
equilibrium or cold nuclear matter, which is important to studying quarkonium
production in heavy ion, proton-ion, and electron-ion collisions.
