Theoretical model for the Mpemba effect through the canonical first-order phase transition
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Published on: September 4, 2015
1School of Physics, Southeast University, Nanjing 211189, China.
Abstract:
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.
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