  We investigate the evolution of the net-proton kurtosis and the kurtosis of
the chiral order parameter near the critical point in the model of
nonequilibrium chiral fluid dynamics. The order parameter is propagated
explicitly and coupled to an expanding fluid of quarks and gluons in order to
describe the dynamical situation in a heavy-ion collision. We study the
critical region near the critical point on the crossover side. There are two
sources of fluctuations: non-critical initial event-by-event fluctuations and
critical fluctuations. These fluctuations can be distinguished by comparing a
mean-field evolution of averaged thermodynamic quantities with the inclusion of
fluctuations at the phase transition. We find that while the initial state
fluctuations give rise to flat deviations from statistical fluctuations,
critical fluctuations reveal a clear structure of the phase transition. The
signals of the critical point in the net-proton and sigma field kurtosis are
affected by the nonequilibrium dynamics and the inhomogeneity of the space-time
evolution but develop clearly.
