  We study the spin-dependent in-medium dynamics of quarkonia by using the
potential nonrelativistic QCD (pNRQCD) and the open quantum system framework.
We consider the pNRQCD Lagrangian valid up to the order $\frac{r}{M^0}=r$ and
$\frac{r^0}{M}=\frac{1}{M}$ in the double power counting. By considering the
Markovian condition and applying the Wigner transformation upon the diagonal
spin components of the quarkonium density matrix with the semiclassical
expansion, we systematically derive the Boltzmann transport equation for
quarkonia with polarization dependence in the quantum optical limit. Unlike the
spin-independent collision terms governed by certain chromoelectric field
correlators, new gauge invariant correlators of chromomagnetic fields determine
the recombination and dissociation terms with polarization dependence at the
order we are working. We also derive a Lindblad equation describing the
in-medium transitions between spin-singlet and spin-triplet heavy
quark-antiquark pairs in the quantum Brownian motion limit. The Lindblad
equation is governed by new transport coefficients defined in terms of the
chromomagnetic field correlators. Our formalism is generic and valid for both
weakly-coupled and strongly-coupled quark gluon plasmas. It can be further
applied to study spin alignment of vector quarkonia in heavy ion collisions.
