  For the understanding of fluctuation measurements in heavy-ion collisions it
is crucial to develop quantitatively reliable dynamical descriptions which take
the non-perturbative nature of QCD near the phase transition into account. We
discuss a novel QCD-assisted transport approach based on non-equilibrium chiral
fluid dynamics and the effective action of low energy QCD. In this framework,
we study the time-evolution of fluctuation measures of the critical mode,
notably the kurtosis, for a non-expanding system. From this, we can estimate
the equilibration times of critical mode fluctuations in the QCD phase diagram.
These allow us to identify both the phase boundary and the critical region near
the QCD critical point.
