  In this proceeding, we study the dynamical evolution of the sigma field
within the framework of Langevin dynamics. We find that, as the system evolves
in the critical regime, the magnitudes and signs of the cumulants of sigma
field, $C_{3}$ and $C_{4}$, can be dramatically different from the equilibrated
ones due to the memory effects near $T_c$. For the dynamical evolution across
the 1st order phase transition boundary, the supercooling effect leads the
sigma field to be widely distributed in the thermodynamical potential, which
largely enhances the cumulants $C_3, \ C_4$, correspondingly.
