  We use a potential model to investigate the phenomenology of quarkonium in a
thermal rotating medium, where vorticity and spin density are not necessarily
in equilibrium. We find that the quarkonium spin density matrix, as well as the
binding energy and melting temperature, are sensitive to both the vorticity and
the lack of equilibrium between vorticity and spin. This means that quarkonium
spin alignment is a sensitive probe for vorticity and spin within the
hydrodynamic phase. Information unequivocably pointing to spin-orbit
non-equilibrium dynamics can be obtained from a combined study of quarkonium
relative abundance and spin alignment, as well as experimentally obtainable
off-diagonal density matrix elements.
