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We study the nonequilibrium dynamics of second-order classical phase transitions in a simplified Ginzburg-Landau model using the Fokker-Planck formalism. In particular, we focus on deriving the Kibble-Zurek scaling laws that dictate the dependence of spatial correlations on the quench rate. In the limiting cases of overdamped and underdamped dynamics, the Fokker-Planck method confirms the theoretical predictions of the Kibble-Zurek scaling theory. The developed framework is computationally efficient, enables the prediction of finite-size scaling functions, and is applicable to microscopic models as well as their hydrodynamic approximations. We demonstrate this extended range of applicability by analyzing the nonequilibrium linear to zigzag structural phase transition in ion Coulomb crystals confined in a trap with periodic boundary conditions.
statistical physics; atomic, molecular and optical; condensed matter, materials and applied physics; general physics