  We derive equations of motion for the reduced density matrix of a heavy
quarkonium in contact with a quark-gluon plasma in thermal equilibrium. These
equations allow in particular a proper treatment of the regime when the
temperature of the plasma is comparable to the binding energy of the
quarkonium. These equations are used to study how the quarkonium approaches
equilibrium with the plasma, and we discuss the corresponding entropy increase,
or free energy decrease, depending on the temperature regime. The effect of
collisions can be accounted for by the generalization of the imaginary
potential introduced in previous studies, and from which collision rates are
derived. An important outcome of the present analysis is that this imaginary
potential has a sizeable dependence on the energy of the relevant transitions.
