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In this proceeding, we investigate the dynamical evolution of the $\sigma$field with a trajectory across the 1st order phase transition boundary, usingLangevin dynamics from the linear sigma model. We find the high order cumulantsof the $\sigma$ field are largely enhanced during the dynamical evolution,compared with the equilibrium values, due to the supercooling effect of thefirst order phase transition.

Enhancements of high order cumulants across the 1st order phase transition boundary