# Dynamical fluctuations in critical regime and across the 1st order phase transition

## TL;DR

This paper investigates the dynamical behavior of the sigma field during critical and first-order phase transitions, revealing significant non-equilibrium effects on cumulants due to memory effects and supercooling.

## Contribution

It introduces a Langevin dynamics framework to study non-equilibrium fluctuations of the sigma field across phase transitions, highlighting the impact of memory effects and supercooling.

## Key findings

- Cumulants of sigma field deviate from equilibrium near T_c
- Supercooling enhances higher-order cumulants
- Memory effects significantly influence dynamical evolution

## Abstract

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.