The Mpemba effect is real. See e.g.
Takada, Hayakawa, Santos, "Mpemba effect in inertial suspensions", Phys. Rev. E 103, 032901, 2021-03-08. The only disagreement is whether it applies to water or not. Given sufficiently rapid cooling in the experimental setup I described in my previous post in this thread, it can be shown to exist in water. Anyone claiming otherwise is not sufficiently aware of the peer-reviewed articles on the subject within the last decade or so. Many papers exist that claim otherwise, but suffer from incorrect assumptions or insufficient cooling rate, and extend the logical result (that the effect does not occur
in these conditions) illogically into "the effect does not exist".
At the core of the real Mpemba effect is that
heat capacity is not constant
in non-equilibrium states.
It is well known that for solids, heat capacity is dependent on the lattice structure. Essentially,
latent heat - energy stored in the material without affecting the temperature of the material –, is associated with the phase change: the change in structure. Water ice itself has at least
nineteen different phases. Note that while many can only be produced in specific (high) pressures, some of them can remain stable well outside their formation range. Given temperature and pressure, there is often more than one stable phase. Indeed, at the triple point, the solid, liquid, and gaseous phases are all in dynamic equilibrium.
For liquid water, the situation is more complicated, because any molecular structures involved are temporary and unstable (with the most stable ones, like
water methane clathrates, involving other molecules), and the really interesting physics involves the properties of individual water molecules; the hydrogen-oxygen bonds (and to a lesser extent, the hydrogen-hydrogen bonds) in non-equilibrium states, when cooled or heated
rapidly.
To simplify what happens in the real Mpemba effect, is that the liquid at hand is far from an equilibrium state, and because of recently been at much higher temperature, can lose heat energy much faster than the same liquid at the same temperature in an equilibrium state would. Simply put, the recently-hot liquid has smaller heat capacity. (The reality is more interesting, especially when the sample starts getting nearer to an equilibrium state of the heat bath, as localized
heating can often be detected due to the latent heat. But close enough for an intuitive understanding, the interesting parts and the actual mechanism, are more like technical details.)
If we had some kind of device or meter that could measure the net energy flow between the heat bath (freezer) and the (originally liquid) sample, we'd find that
at the same temperature, the energy flow from the recently-hot sample to the heat bath is higher
than for the sample that was not originally that hot.
In other words, there is nothing really odd here, just a variation in the heat capacity, depending on whether the water sample was really hot (boiling) or not. Nothing
anomalous in the everyday life sense, just an interesting physical phenomena.
I am actually a materials physicist (or close enough; I never submitted my thesis on ferrochrome structure providing the corrosion resistance effects), specialized in the numerical simulation aspects. The Mpemba effect is interesting, because it was only in the last decade or so that we could numerically simulate the effect; and do so with multiple different classical chemical force-field potential models. (Because of the large number of electrons involved [two per molecule, with hundreds of molecules minimum needed due to periodic boundary conditions inherent in ab initio simulations], and the difficulties in modeling hot water in
ab initio simulations, the entire phenomenon hasn't been simulated ab initio (using e.g. VASP, Dalton, Siesta, or similar) thus far, only at specific temperatures showing the differences in the molecular structure of each water molecule, supporting the observations in simulations using classical force-field models.)