Landau theory for the Mpemba effect through phase transitions

The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at colder temperature. In many of experimental observations effect, e.g. water and clathrate hydrates, it defined by phase transition timing. However, none theoretical investigations so far considered timing transition, most abstract models used to explore do not have transition. We use phenomenological Landau theory for transitions identify second order time, demonstrate with concrete example can exist such models.