Hot Water Freezes Faster Than Cold? A 2,000-Year Puzzle Gets Its Clearest Answer
In 1963, 13-year-old Erasto Mpemba, a student at Magamba High School in Tanzania, put a still-boiling milk-and-sugar mixture straight into the freezer because no space was available for cooled mixtures. His ice cream froze first. Mocked by his physics teacher—"That must be Mpemba physics, not universal physics"—he persisted, and after Professor Denis Osborne of the University of Dar es Salaam verified the observation, they published in *Physics Education* in 1969. Thus was named the Mpemba effect: under certain conditions, hot water freezes faster than cold water.
Mpemba had unknowingly rediscovered a puzzle over two thousand years old:
- Aristotle (*Meteorology*, 4th century BCE): water that has been heated cools faster, which is why people warm water in the sun to cool it quickly.
- Francis Bacon (*Novum Organum*, 1620): "aqua parum tepida facilius conglacietur quam omnino frigida" — slightly warm water freezes more easily than completely cold water.
- René Descartes (*Les Météores*, 1637): water that has long been kept on a fire freezes faster than other water.
- Evaporation: hot water loses mass, leaving less to freeze
- Convection: stronger circulation speeds heat transfer to the surface
- Supercooling: heating alters nucleation behavior of impurities; cold water can supercool further below 0°C
- Hydrogen bonds: heating disrupts water's hydrogen-bond network, causing a "lag" upon rebuilding
- Frost melting: hot water melts freezer frost, improving contact with metal
- **2020, *Nature* (Kumar & Bechhoefer, Simon Fraser University): laser-manipulated colloidal beads in an engineered energy landscape confirmed exponentially faster relaxation from higher initial temperatures.
- 2024, *Physical Review Letters* (Weizmann team incl. Raz): a quantum inverse Mpemba effect on a single trapped strontium ion qubit—a cold qubit heats exponentially faster than a hot one (strong version), a pure quantum-interference effect requiring strong coherence.
- Quenched from the paramagnetic phase: overlap with the staggered mode is zero—the system never excites its slowest bottleneck mode and relaxes quickly.
- Quenched from the antiferromagnetic ordered phase: the initial structure closely resembles the slow mode, so the system "inherits" a large slow-mode amplitude and carries a long relaxation tail.
- Blom et al., *Strong Mpemba Effect Through a Reentrant Phase Transition*, arXiv:2604.28117 (2026)
- Lu & Raz, *Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse*, PNAS 114, 5083 (2017)
- Kumar & Bechhoefer, *Exponentially faster cooling in a colloidal system*, Nature 584, 64 (2020)
- Klich et al., *The Mpemba index and anomalous relaxation*, arXiv:1711.05829
- Holtzman & Raz, *Landau Theory for the Mpemba Effect Through Phase Transitions*, arXiv:2204.03995
- Aharony Shapira et al., *Inverse Mpemba Effect Demonstrated on a Single Trapped Ion Qubit*, PRL 133, 010403 (2024)
- Mpemba & Osborne, *Cool?*, Physics Education 4, 172 (1969)
Why Is It So Hard to Explain?
Newton's law of cooling suggests the effect is absurd: the hotter object should take longer to reach freezing. Yet experiments show it can occur. Proposed mechanisms over the decades include:
In 2012 the Royal Society of Chemistry offered a £1,000 prize, receiving over 22,000 entries. Winner Nikola Bregović identified evaporation, dissolved gases, convection, and supercooling—considering supercooling key—but noted the effect only appears when cold water's spontaneous nucleation temperature is several degrees lower. The core problem: no universal explanation covers all cases; the effect appears and disappears unpredictably.
A Paradigm Shift (2017)
Zhiyue Lu (UNC) and Oren Raz (Weizmann Institute), publishing in PNAS, asked a more fundamental question: do any thermodynamic laws forbid a system farther from equilibrium from relaxing faster than one starting nearby? Their answer: no. Using a Markovian non-equilibrium statistical mechanics framework, they showed that hotter systems can explore more configurations and stumble upon "shortcuts"—intermediate states that bypass the bottlenecks cold systems must traverse.
> "We all have a naive picture that temperature should vary monotonically... but for a system driven out of equilibrium, it's not accurate to say it 'has a temperature.' Then you can take strange shortcuts." — Oren Raz
The Mpemba effect is not a quirk of water, but a general feature of non-equilibrium relaxation.
From Beads to Qubits
But none of these addressed systems that undergo a phase transition—like water freezing.
Reentrant Phase Transitions: The Key
A new arXiv paper addresses exactly this:
"Strong Mpemba Effect Through a Reentrant Phase Transition"** *Kristian Blom, Doron Benyamin, Uwe Thiele, Oren Raz, Aljaz Godec* arXiv: 2604.28117
The setting is the antiferromagnetic Ising model in a uniform external field. Its phase diagram features a reentrant phase transition: at fixed temperature, increasing the field takes the system ordered → disordered → ordered again, crossing the phase boundary twice.
The Secret: The Slowest Mode
After a quench, fluctuation modes decay at different rates; the slowest mode sets the relaxation time. In the paramagnetic phase of this model, the slowest mode is purely staggered (neighboring sites oscillate in opposite phase). The crucial question is the overlap between the initial state and this mode:
The result: the system starting from the hotter paramagnetic phase relaxes far faster than one from the cold ordered phase—in the strong Mpemba effect, relaxation times drop by a jump, exponentially.
The Decisive Control Experiment
The authors varied the lattice coordination number. Past a threshold, the reentrant phase transition disappears—and the Mpemba effect disappears simultaneously. This "you can't have one without the other" causal chain establishes that the reentrant transition is a necessary condition for the strong Mpemba effect in this framework.
From Checkerboard to Freezer
The Ising model does not directly explain water—it has no hydrogen bonds, fluid dynamics, or nucleation chemistry. But it reveals a universal principle:
> In non-equilibrium relaxation, the system's "memory"—the overlap between its initial state and relaxation modes—determines its route to equilibrium. When that overlap is zero, the system bypasses the slowest bottleneck and relaxes exponentially faster.
For water, this suggests a concrete research direction: perhaps certain fluctuation modes of liquid water are orthogonal to the slowest ice-nucleation modes, letting water from a specific initial temperature bypass the nucleation bottleneck.
The Bigger Picture
Equilibrium statistical mechanics—Boltzmann, Gibbs, Onsager, Wilson—is one of physics' crowning achievements, yet the real world (cooling coffee, discharging batteries, turbulent atmospheres, molecular motors) is almost never at equilibrium. Non-equilibrium statistical mechanics remains immature. The Mpemba effect strikes at its core questions: how do systems relax? How is initial condition encoded in the relaxation path? Is there an optimal path?
Epilogue: The Ice Cream Boy's Legacy
Erasto Mpemba passed away around 2023. He never published another paper, working in Tanzania's wildlife service. But his name is permanently inscribed in physics.
The takeaway for the perennial debate:
> It is not a simple yes-or-no question. Under some conditions, yes—hot freezes faster. Under others, even the inverse effect occurs (cold heating faster). It depends on the system's "memory": which phase it starts from, and whether that phase resonates with the slowest relaxation mode. When the resonance is zero, the system finds a shortcut around every traffic jam.
Physics' beauty often lies not in obvious truths, but in counterintuitive exceptions. The Mpemba effect reminds us that even the most everyday phenomena may hide doors to unknown worlds.