One afternoon in 1963, 13-year-old Erasto Mpemba was making ice cream at Magamba Secondary School in Tanzania. In a hurry to claim space in the freezer, he stuck in his slurry of milk and sugar while it was still piping hot—unlike his classmates, who had left their batches out to cool beforehand. Yet, in an event that would shape the course of modern physics, Mpemba found that his ice cream froze first.
Mpemba later repeated the experiment with water and kept asking his teachers why hot liquids froze faster than cold ones, but they brushed him off. Undeterred, Mpemba decided to ask Denis Osborne, a physicist visiting from the University of Dar es Salaam. Osborne promised to go home and repeat the experiment himself. In a now-classic 1969 paper, Osborne—crediting Mpemba as first author—reported the phenomenon, proclaiming that “no question should be ridiculed.”
It turns out water was only the tip of the iceberg. Over the past decade, scientists have uncovered similar “Mpemba effects” in a zoo of different materials—from crystallizing polymers to magnets. More recently, the effects have turned up in the quantum realm, such as single ions suspended with lasers. Now, a new theoretical framework, published today in Physics Review X, stitches the assorted Mpemba effects together. It explains how, in each case, a system that’s pushed farther from equilibrium can find a quicker path back to a steady state. “All these effects you might think of as completely different are actually sort of the same thing,” says John Bechhoefer, a physicist at Simon Fraser University.
To this day, researchers debate whether the Mpemba effect is generally true for water. Water turns out to be particularly hard to study: Its freezing conditions depend on small differences, such as the presence of dissolved gases and the smoothness of the container.
But scientists see clearer signs of the Mpemba effect in other materials. For instance, both clathrate hydrates, cagelike structures of water molecules used for carbon capture, and the polylactide plastic used for 3D printing recrystallize faster when first brought to higher temperatures. Scientists also found a magnetic analog: Some materials that start with a stronger magnetic field can be demagnetized faster. “It became clear that this is a very generic phenomenon—it’s everywhere,” says John Goold, a physicist at Trinity College Dublin. “If you start looking for it, you’ll find it.”
One general mathematical explanation for the effect came in a 2017 study from Oren Raz at the Weizmann Institute of Science and Zhiyue Lu of the University of North Carolina at Chapel Hill. They mapped out all the different ways a simple system of particles can evolve toward equilibrium. The work showed that when systems are farther from equilibrium, they can explore more paths to the target state. “You can get really surprising shortcuts,” Raz says. “Away from equilibrium, your initial intuition completely collapses.”
The explanation gained further credibility in 2020 when Bechhoefer and colleagues showed it in action, with rolling microscopic glass beads submerged in water. They measured how long it took for fast (hot) and slow (cold) beads to settle in a hilly underwater landscape. They found that some of the hot beads came to a resting place significantly faster than the cold beads. They also used the setup to demonstrate the “inverse Mpemba effect”—in which an initially colder substance heats up faster.
But just as scientists began to close in on the Mpemba mechanism in ordinary materials, the phenomenon turned up in an entirely new domain: the quantum world of atoms.
In 2023, Raz’s Ph.D. student Shahaf Aharony Shapira wanted to collaborate with her husband, Yotam Shapira, who was completing his Ph.D. on quantum computation. Raz told the couple to look for hints of the Mpemba effect in single ions trapped with lasers. To their surprise, they found that the cold ions heated up faster than hot ones: a clear case of the inverse Mpemba effect. Around the same time, another team in China stumbled across the normal Mpemba effect in a similar system.
Meanwhile, Sara Murciano at Paris-Saclay University was studying a mathematical model of how magnetic fields in quantum systems reorganize after being disturbed. Strangely, the more asymmetrical the magnetic field was initially, the faster the system regained its symmetry locally. She was befuddled and suspected a bug in her code—until a visiting professor told her about Mpemba. Murciano teamed up with experimentalists in Austria, who took a chain of 12 trapped ions, tilted their magnetic spins to varying degrees, and clocked how quickly they snapped back into place, confirming the prediction.
All three teams posted preprints of their findings in early 2024, launching a surge of interest in quantum Mpemba effects—and how all these effects might relate to one another.
Now, Goold and colleagues have identified what he calls “one ring to rule them all”—a common framework to describe various classical and quantum Mpemba effects. They borrowed a tool from quantum information theory, which describes how systems evolve in terms of how they consume a particular resource. In each case, a system that requires more of a certain resource—be it temperature fluctuations or magnetic asymmetries—to reach a target state can nevertheless reach it faster. Because systems very far from equilibrium tend to follow different rules, they can feature special configurations in which the slowest routes to equilibrium cancel out—allowing them to eat up resources unusually quickly to reach equilibrium faster. “He really managed to put everything under the same umbrella,” Murciano says.
Bechhoefer says casting these effects in the same language may help guide the search for “manifestations that you might not notice if you didn’t have this way of seeing the world.” Furthermore, shortcuts to equilibrium are not just curios of nature; if scientists can identify the initial conditions that give rise to Mpemba effects, they could optimize all kinds of processes.
Physicists have already begun to explore how Mpemba effects could make cooling and heating schemes more efficient. Some have suggested they could also improve atomic force microscopy, by controlling the temperature of the imaging tip, and aid a technique for producing ceramic materials using the pressure generated as water freezes. In the quantum realm, the effects could help speed up quantum computations and the preparation of quantum states. “So far, we have tried to extract the physics—why, if, and when it occurs,” Murciano says. “Now, we have to exploit the physics.”
Doing so won’t be easy—it will require mapping out all the possible evolution pathways for a system. Yet Krissia Zawadzki, a physicist at the São Carlos Institute of Physics, thinks a new Mpemba revolution is on the horizon. Her team recently spotted another quantum Mpemba effect by examining how the nuclear spins of atoms relax in a solution of liquid chloroform. They showed that the effect could be harnessed by a solid-state refrigerator—like those being designed to cool quantum computing chips—to increase its cooling power by about 10%. “In principle we know how to reach the special initial conditions,” Zawadzki says. “This demonstration makes it clear that it’s feasible” to apply Mpemba in the real world.
She finds a deeper lesson in the Mpemba story, too. It’s a reminder how basic curiosity about nature’s oddities can unlock surprisingly deep insights—which sometimes work out in your favor, she says. “That can just be cooling ice cream faster [or] making quantum technologies more efficient.”