  We study thermalization by applying gradient expansion to the Kadanoff-Baym
equations of the 2PI effective action to two-loop in a theory with Dirac
fermions coupled to scalars. In addition to those chemical potentials which
equilibrate in the on-shell limit, we identify modes which are conserved in
this approximation, but which relax when off-shell effects are taken into
account. This implies that chemical equilibration does not require higher loop
contributions to the effective action and is compatible with the gradient
expansion. We explicitly calculate the damping time-scales of both, on- and
off-shell, chemical equilibration rates. It is shown that off-shell
equilibration is suppressed by the thermal width of the particles in the
plasma, which explains the separation of on- and off-shell chemical
equilibration time-scales.
