  In studies of the QCD deconfining phase transition or cross-over by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. In this paper we extend our previous
study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model,
which serves as an effective model for some QCD properties. We investigate the
linear theory of spinodal decomposition in some detail. It describes the early
time evolution of the 3D model under a quench from the disordered into the
ordered phase well, but fails in 2D. Further, the quench leads to competing
vacuum domains, which are difficult to equilibrate, even in the presence of a
small external magnetic field. From our hysteresis study we find, as before, a
dynamics dominated by spinodal decomposition. There is evidence that some
effects survive in the case of a cross-over. But the infinite volume
extrapolation is difficult to control, even with lattices as large as $120^3$.
