-Goureesankar Sathyanath

Suppose we provide you with two containers having equal volumes of water, with one hotter than the other, and ask you to predict which one will freeze first. The answer would seem quite obvious - the colder one. But you would be wrong! No, we’re not crazy nor are the thermodynamic laws wrong - this is called the Mpemba effect.

While such an effect was thought to be common knowledge since the times of Aristotle, it became highly popularized in 1963 after a curious observation by Erasto Bartholomeo Mpemba, a schoolboy from Tanzania. In his cooking class, he noticed that a hot ice cream mix froze faster than a cold one.

When Dr. Denis Osborne visited his school, he posed the question "If you take two similar containers with equal volumes of water, one at 35 °C (95 °F) and the other at 100 °C (212 °F), and put them into a freezer, the one that started at 100 °C (212 °F) freezes first. Why?".

However, this phenomenon is much more than the cold (...pun definitely unintended) fact that “hot water freezes faster than cold water”. More precisely, it is stated as: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner." Aristotle has also described people warming water in the sun in order to freeze it more efficiently.

The Mpemba effect can be demonstrated with an Ising model of two magnetic materials. The particles on each point on the 2D grid can have spin up or spin down with neighbours having the same spin as to have lower energy. If cooled below the Curie temperature, they form a well-ordered ferromagnet.

If we take two non magnetic materials and place them in a cold heat bath below the Curie temperature, their spins line up and lose excess energy to the bath. If the hot system magnetizes before the cold one, viola! the Mpemba effect again!

In 2017, a group of researchers predicted an “Inverse Mpemba” effect, in which heating a cooled, far-from-equilibrium system took less time than a hotter, near-equilibrium system. Some proposed explanations for the inverse effect have to deal with diffusion dynamics. However, explanations for the Mpemba effect have been blowing hot and cold.

While some argue this is due to the deviation of the velocity distribution from the Maxwell-Boltzmann distribution, others say it is due to the supercooling of hydrogen bonds and molecular dynamics. There are also many skeptics who do not fully believe this concept. Safe to say, the Mpemba effect is a hot topic of interest.

References:

https://math.ucr.edu/home/baez/physics/General/hot_water.html

https://en.m.wikipedia.org/wiki/Mpemba_effect