The Mpemba effect for phase transitions by Landau theory

The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We show how one can define the phase transition time in a non-equilibrium state using the Landau theory for phase transitions. With this definition, we show that a Mpemba effect with respect to phase transitions can exist in such models, namely that the hotter system undergoes the transition before the colder one when quenched to a cold temperature.