  Starting from the (Polyakov-) Nambu-Jona-Lasinio Lagrangian, (P)NJL, we
formulate a transport theory which allows for describing the expansion of a
quark-antiquark plasma and the subsequent transition to the hadronic world
--without adding any new parameter to the standard (P)NJL approach, whose
parameters are fixed to vacuum physics. This transport theory can be used to
describe ultrarelativistic heavy-ion reaction data as well as to study the
(first-order) phase transition during the expansion of the plasma. (P)NJL
predicts such a phase transition for finite chemical potentials. In this
contribution we give an outline of the necessary steps to obtain such a
transport theory and present first results.
