Non-equilibrium cumulants within model A near the QCD critical point

We study the non-equilibrium cumulants of the $\sigma$ field in the phase transition region via Langevin dynamics. Cumulants up to fourth-order have been calculated based on the spacetime-dependent $\sigma$ configurations from the event-by-event numerical simulations. By limiting the cooling of the system in a Hubble-like way, the out-of-equilibrium cumulants illustrate clear memory effects during the evolution. Both the signs and the magnitudes of the high-order cumulants differ from the equilibrium ones below the phase transition temperature. At the same time, the dynamical cumulants grow more intensively from the first-order phase transition side than they do from the crossover side. In addition, analysis of the high-order off-equilibrium cumulants on the hypothetical freeze-out lines present non-monotonic curves in the critical region.