  After a rapid increase in temperature across the deconfinement temperature
T_d to temperatures T >> T_d, pure gauge theories exhibit unstable long
wavelength fluctuations in the approach to equilibrium. This phenomenon is
analogous to spinodal decomposition observed in condensed matter physics, and
also seen in models of disordered chiral condensate formation. At high
temperature, the unstable modes occur only in the range 0 < k < k_c, where k_c
is on the order of the Debye screening mass m_D. Equilibration always occurs
via spinodal decomposition for SU(2). For SU(3) at T near T_d, nucleation
replaces spinodal decomposition as the dominant equilibration mechanism. Monte
Carlo simulations of SU(2) and SU(3) lattice gauge theories exhibit the
predicted phenomena. For SU(2), the observed value of k_c is in reasonable
agreement with a value predicted from previous lattice measurements of m_D.
