  The dynamics of 2d Potts models, which are temperature driven through the
phase transition using updating procedures in the Glauber universality class,
is investigated. We present calculations of the hysteresis for the (internal)
energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used
to define finite volume estimators of physical observables, which can be used
to study the approach to the infinite volume limit. We compare with equilibrium
configurations and the preliminary indications are that the dynamics leads to
considerable alterations of the statistical properties of the configurations
studied.
