Mpemba’s paradox: explaining why hot freezes faster than cold changes thermodynamics

Japanese researchers from Kyoto University proposed a universal criterion to assess the Mpemba effect, which means that hot systems freeze faster than colder ones under the same conditions.

This effect is believed to have been first observed by Aristotle more than 2,000 years ago. It was rediscovered by Tanzanian student Erastus Mpemba in 1963. It happened when he was making ice cream in one of his culinary classes. He asked a local physics teacher to explain, why the hot ice cream mixture in the refrigerator froze faster than the cold one, but the teacher just laughed at him.

Later, Mpemba asked Dennis Osborne, a professor of physics at the University of Dar es Salaam, the same question. Subsequently, Mpemba and Osborne jointly published an article describing a similar paradox using ordinary water as an example.

They also found out that the Mpemba effect applies not only to water and simple liquids. They also have been observed in other systems under a microscope. However, the detection of this paradox critically depends on the choice of the distance measure used to determine how far the system is from equilibrium.

Because there are an infinite number of possible distance measures, the effect observed using one measure, may not appear for any finite time using another. Traditionally, the relaxation rate, which determines the rate at which the system returns to equilibrium after a temperature change, is usually estimated using a single monotonic measure. However, in this case, false or contradictory results can be obtained.

This led Japanese researchers to develop a universal criterion for determining the manifestation of the Mpemba effect. This criterion does not rely on any single indicator, but rather on the theory of thermomajority — a mathematical structure that combines different measures of distance.

Using this theory helped Japanese researchers determine an accurate criterion for assessing the rate of thermal relaxation, eliminating the ambiguities that arose in previous studies. The researchers also determined that the effect is not limited to a specific temperature range but can occur in a wide range of temperature conditions.

Based on this, the Japanese researchers suggested a new look at the fundamental principles, that control the dynamics of thermal relaxation, as well as potential applications for improving the efficiency of thermal engines and cooling technologies. According to them, the key question remains: on what minimum time scale can the Mpemba thermal majorization effect manifest itself? Investigating this aspect through the prism of velocity limits may help to establish fundamental limits on the relaxation dynamics.

The study was published in the journal Physical Review Letters

Source: SciTechDaily