  Based on the 2PI quantum effective action of the linear sigma model with
constituent quarks, we develop a transport approach to study systems out of
equilibrium. In particular, we focus on the chiral phase transition as well as
the critical point, where nonequilibrium effects near the phase transition give
rise to critical behavior such as the fluctuation of the baryon number density.
Predictions for long-range correlations and fluctuations of observables in our
model could be used to study fundamental properties of the QCD phase
transition. In the previous version of our transport model the chiral fields
are implemented as mean fields, whereas quarks are treated as on-shell
particles in the Vlasov equation with a dynamical force term. The current
update includes also the distribution functions of sigma mesons and pions in a
self-consistent way. On this basis a dissipation kernel between the mean fields
and particle modes can be implemented.
