  The kinetics of the chiral phase transition is studied within a linear
quark-meson-$\sigma$ model, using a Monte-Carlo approach to semiclassical
particle-field dynamics. The meson fields are described on the mean-field level
and quarks and antiquarks as ensembles of test particles. Collisions between
quarks and antiquarks as well as the $q\overline{q}$ annihilation to $\sigma$
mesons and the decay of $\sigma$ mesons is treated, using the corresponding
transition-matrix elements from the underlying quantum field theory, obeying
strictly the rule of detailed balance and energy-momentum conservation. The
approach allows to study fluctuations without making ad hoc assumptions
concerning the statistical nature of the random process as necessary in
Langevin-Fokker-Planck frameworks.
