Dynamical and finite-size effects on the signal of first-order phase transition

We study the dynamical behaviors of the criterion identifying the first-order phase transition in the matter generated by the relativistic heavy-ion collisions, by explicitly involving the dynamical effects based on the Fokker-Plank framework. The perspectives we taken into account range from phase transition scenarios, initial temperatures, volume effect, relaxation rates, and evolution trajectories. Our numerical calculations show that the dynamical signal of the first-order phase transition can be reserved in certain conditions. Besides the delaying effects due to a finite relaxation time, a larger initial temperature, a smaller volume, a larger relaxation rate, or bending of the trajectory will lead to reduction of the signal. Our discussions on the criterion offer valuable reference information for the experimental detection of the first-order phase transition signal.