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We derive a coupled set of equations that describe the non-equilibriumevolution of cumulants of critical fluctuations for space-time trajectories onthe cross-over side of the QCD phase diagram. In particular, novel expressionsare obtained for the non-equilibrium evolution of non-Gaussian Skewness andKurtosis cumulants. Utilizing a simple model of the space-time evolution of aheavy- ion collision, we demonstrate that, depending on the relaxation rate ofcritical fluctuations, Skewness and Kurtosis can differ significantly inmagnitude as well as in sign from equilibrium expectations. Memory effects areimportant and shown to persist even for trajectories that skirt the edge of thecritical regime. We use phenomenologically motivated parameterizations offreeze-out curves, and of the beam energy dependence of the net baryon chemicalpotential, to explore the implications of our model study for the criticalpoint search in heavy-ion collisions.

Real time evolution of non-Gaussian cumulants in the QCD critical regime