  The beam energy scan program at RHIC provides data on net-proton number
fluctuations with the goal to detect the QCD critical end point and first-order
phase transition. Interpreting these experimental signals requires a vital
understanding of the interplay of critical phenomena and the nonequilibrium
dynamics of the rapidly expanding fireball. We study these aspects with a fluid
dynamic expansion coupled to the explicit propagation of the chiral order
parameter sigma via a Langevin equation. Assuming a sigma-proton coupling
through an effective proton mass, we relate cumulants of the order parameter
and the net-proton number at freeze-out and obtain observable cumulant ratios
as a function of beam energy. We emphasize the role of the nonequilibrium
first-order phase transition where a mixed phase with gradual freeze-out can
significantly alter the cumulants. We find that the presence of a critical end
point is clearly visible in the cumulant ratios for a relatively wide range of
center-of-mass energies.
