The Mpemba effect is the phenomenon in which the system with high initial temperature cools faster than the system with low initial temperature when all other conditions are the same. A theoretical model of the Mpemba effect through the canonical first-order phase transition is proposed in this paper, which shows that in the cooling processes, the path of the first-order phase transition of the system with the high initial temperature does not pass through any metastable state, while the path of the first-order phase transition of the system with the low initial temperature passes through a metastable state, which leads to the occurrence of the Mpemba effect. Then an example of the theoretical model is given in the Blume-Emery-Griffiths model. The Monte Carlo algorithm is adopted to calculate the estimated times for both systems with different initial temperature to cool down and undergo a first-order phase transition. The simulation results demonstrate a Mpemba effect in the system. Moreover, the evolution paths of the first-order phase transitions of the systems with high and low initial temperatures are given, respectively. The theoretical model presented here may help explain the Mpemba effect in water.

中文翻译：

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通过典型一阶相变的 Mpemba 效应的理论模型

Mpemba 效应是在所有其他条件相同的情况下，初始温度高的系统比初始温度低的系统冷却得更快的现象。本文提出了通过典型一阶相变的 Mpemba 效应理论模型，表明在冷却过程中，初始温度较高的系统的一阶相变路径不通过任何亚稳态，而初始温度较低的系统的一阶相变路径经过亚稳态，从而导致Mpemba效应的发生。然后在 Blume-Emery-Griffiths 模型中给出了理论模型的一个例子。采用蒙特卡罗算法计算两个初始温度不同的系统冷却并经历一阶相变的估计时间。仿真结果表明系统中存在 Mpemba 效应。此外，分别给出了初始温度高、初始温度低的系统一级相变的演化路径。这里提出的理论模型可能有助于解释水中的 Mpemba 效应。