  We report on progress in the nonperturbative understanding of quarkonium
dynamics inside a thermal plasma. The time evolution of small-size quarkonium
is governed by two-point correlation functions of chromoelectric fields dressed
with an adjoint Wilson line, known in this context as generalized gluon
distributions (GGDs). The GGDs have been calculated in both weakly and strongly
coupled plasmas by using perturbative and holographic methods. Strikingly, the
results of our calculations for a strongly coupled plasma indicate that the
quarkonium dissociation and recombination rates vanish in the transport
descriptions that assume quarkonium undergoes Markovian dynamics. However, this
does not imply that the dynamics is trivial. As a starting point to explore the
phenomenological consequences of the result at strong coupling, we show a
calculation of the $\Upsilon(1S)$ formation probability in time-dependent
perturbation theory. This is a first step towards the development of a
transport formalism that includes non-Markovian effects, which, depending on
how close the as of yet undetermined nonperturbative QCD result of the GGDs is
to the strongly coupled $\mathcal{N}=4$ SYM result, could very well dominate
over the Markovian ones in quark-gluon plasma produced at RHIC and the LHC.
