Hot water freezes first: Uncovering the mysteries of the Mpemba effect
- Date:
- March 21, 2025
- Source:
- Kyoto University
- Summary:
- The Mpemba effect, in which hot systems cool faster than cold ones under the same conditions, was first described by Aristotle more than 2,000 years ago. In 1963 it was rediscovered by Tanzanian student Erasto Mpemba, who observed it when preparing ice cream in a cooking class at school. Mpemba later collaborated with a British physicist on a paper that described its effect on water. Since this influential research, further studies have demonstrated that the effect extends beyond simple liquids and can be observed in a variety of physical systems --even microscopic ones.
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The Mpemba effect, in which hot systems cool faster than cold ones under the same conditions, was first described by Aristotle more than 2,000 years ago. In 1963 it was rediscovered by Tanzanian student Erasto Mpemba, who observed it when preparing ice cream in a cooking class at school. Mpemba later collaborated with British physicist Denis Osborne on a paper that described its effect on water.
Since Mpemba and Osborne's influential research, further studies have demonstrated that the effect extends beyond simple liquids and can be observed in a variety of physical systems -- even microscopic ones. Yet one fundamental challenge has persisted; the detection of the Mpemba effect depends on the choice of a specific distance measure.
An infinite number of distance measures exist, so observing the effect using one distance measure may not materialize within a finite time when evaluated with another. Conventional methods typically assess relaxation speed, which is the rate of return to equilibrium after a change in temperature -- by using a single monotone measure -- but this often leads to inconsistent results.
These pitfalls motivated a team of researchers at Kyoto University to develop a universal criterion for determining the presence of the Mpemba effect: one that does not rely on a single measure. Their approach uses thermomajorization theory, a mathematical framework that unifies different distance measures.
"Our study proves that the use of thermomajorization is equivalent to considering all monotone measures simultaneously," says corresponding author Tan Van Vu.
By employing this theory, Vu and his colleague Hisao Hayakawa were able to provide a rigorous criterion for evaluating thermal relaxation speed, eliminating ambiguities in previous studies and establishing an unambiguous framework for measuring the Mpemba effect.
The team's research also led to the intriguing discovery that the effect is not restricted to a specific temperature range, but can emerge across a wide spectrum of thermal conditions.
"This surprising result suggests that the Mpemba effect reflects a more universal underlying mechanism than previously thought," continues Vu.
In uncovering these mysteries, the group's findings offer new insights into the fundamental principles governing thermal relaxation dynamics, as well as having potential application in enhancing the efficiency of heat engines and cooling technologies. The fields of quantum computing and biophysics stand to benefit as well.
According to Vu and Hayakawa, however, one important question remains: what is the minimum timescale at which the thermomajorization Mpemba effect can occur? Investigating this aspect through the lens of speed limits could help establish fundamental constraints on relaxation dynamics.
Story Source:
Materials provided by Kyoto University. Note: Content may be edited for style and length.
Journal Reference:
- Tan Van Vu, Hisao Hayakawa. Thermomajorization Mpemba Effect. Physical Review Letters, 2025; 134 (10) DOI: 10.1103/PhysRevLett.134.107101
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