The Mpemba Effect: Hot Water Can Freeze Faster Than Cold — A 2,000-Year-Old Puzzle Gets Its Clearest Answer Yet
The story of Erasto Mpemba
In 1963, at Magamba Secondary School in Tanzania, 13-year-old Erasto Mpemba was making ice cream in a cooking class. Finding no room left in the freezer for his boiled milk-and-sugar mixture to cool, he put it in while still scalding hot. To everyone's astonishment, his ice cream froze first. His physics teacher mocked him publicly: "That must be Mpemba physics, not universal physics."
Mpemba persisted. Years later, he raised the question after a lecture by Professor Denis Osborne of the University of Dar es Salaam. Osborne repeated the experiment, confirmed the observation, and in 1969 they published together in *Physics Education*. Thus was named the Mpemba effect: under certain conditions, hot water freezes faster than cold.
A two-thousand-year echo
The puzzle is far older than Mpemba:
- Aristotle (*Meteorology*, 4th century BC): water that has been heated cools and freezes faster.
- Francis Bacon (*Novum Organum*, 1620): "aqua parum tepida facilius conglacietur quam omnino frigida" — slightly lukewarm water freezes more easily than entirely cold.
- Descartes (*Les Météores*, 1637): water kept long over a fire freezes faster than any other.
- Evaporation: hot water loses mass faster, leaving less to freeze.
- Convection: stronger convection improves heat transfer to the surface.
- Supercooling: heating changes nucleation temperatures of impurities; cold water may supercool further below 0°C.
- Hydrogen bonds: heating disrupts the hydrogen-bond network, imposing a "lag" on reformation.
- Frost melting: hot water melts freezer frost, improving contact with metal.
- **2020, *Nature*: John Bechhoefer and Avinash Kumar (Simon Fraser University) used laser-tweezed colloidal beads in a designed energy landscape and observed exponentially faster cooling from higher initial temperatures.
- 2024, *Physical Review Letters*: a Weizmann team (including Raz) demonstrated an inverse quantum Mpemba effect on a single trapped strontium-ion qubit — a cold qubit heated exponentially faster than a hot one, a purely quantum-interference effect requiring strong coherence.
- Quenching from the paramagnetic phase: its overlap with the purely staggered slow mode is zero — the system never excites the bottleneck mode at all.
- Quenching from the antiferromagnetic ordered phase: the structure closely resembles the slow mode, so the system "inherits" a large slow-mode excitation 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: a hotter object should take longer to reach freezing. Yet experiments confirm it sometimes exists. Proposed mechanisms include:
In 2012, the UK's Royal Society of Chemistry offered a £1,000 prize for the best explanation, drawing over 22,000 entries. Winner Nikola Bregović (University of Zagreb) highlighted evaporation, dissolved gases, convection, and especially supercooling as key — but admitted the effect only appears when the cold water's spontaneous nucleation temperature is several degrees lower. The core problem: no universal explanation covers all cases, and the effect's unpredictability makes many suspect experimental artifacts.
A disruptive new perspective (2017)
Zhiyue Lu (UNC) and Oren Raz (Weizmann Institute) reframed the question in PNAS: is any thermodynamic law forbidding 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 a hotter system can access configurations that reveal "shortcuts" bypassing the bottlenecks a colder system must traverse. As Raz put it, a driven non-equilibrium system doesn't truly "have a temperature" — so it can take strange shortcuts.
The implication is revolutionary: the Mpemba effect is not a quirk of water but a generic feature of non-equilibrium relaxation.
From microbeads to qubits
But all these systems either lacked phase transitions or didn't center on them. The classic case — relaxation through a phase transition, like water freezing — remained theoretically murky.
Reentrant phase transitions: the key
A 2026 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 stage is the antiferromagnetic Ising model: spins on a lattice prefer anti-alignment with neighbors, under a uniform external field and coupled to a heat bath. With increasing field at fixed temperature, the system can go ordered → disordered → ordered, crossing the phase boundary twice — a reentrant phase transition.
The secret lies in the slowest mode
When the system is quenched to a new temperature and field, different 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 fluctuations oscillate in antiphase).
Result: the system starting from the hotter paramagnetic phase relaxes exponentially faster — a strong Mpemba effect, where the hotter system finds a shortcut around the slow-mode bottleneck.
A decisive control experiment
The authors varied the lattice coordination number. Beyond a threshold, the reentrant phase transition disappears — and the Mpemba effect vanishes with it. This tight correlation shows the reentrant transition is (within the Ising framework) the necessary and sufficient mechanism for the strong Mpemba effect.
From checkerboards to freezers
The Ising model does not directly explain water freezing, which involves hydrogen bonds, supercooling, convection, and dissolved gases. But it reveals a universal principle:
> In non-equilibrium relaxation, a system's "memory" — the overlap between its initial state and its 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 that at certain temperatures the liquid's fluctuation modes may be orthogonal to the slowest ice-nucleation modes — pointing toward future experimental searches.
The bigger picture
Equilibrium statistical mechanics — Boltzmann, Gibbs, Onsager, Wilson — is one of physics' crowning achievements, yet the real world is almost never in equilibrium. Non-equilibrium statistical mechanics remains immature. The Mpemba effect matters because it probes its core questions: how does a system relax to equilibrium, how are initial conditions encoded in relaxation paths, and do "optimal paths" exist? Blom et al. show that near reentrant transitions, a system's initial "identity" can determine its relaxation speed almost topologically.
Epilogue
Erasto Mpemba died around 2023. He worked in Tanzania's wildlife administration and never published another scientific paper — but his name is permanently inscribed in physics. The new work is not the final answer, but it is a milestone: the first clear mechanistic link between phase transitions, reentrant behavior, and the strong Mpemba effect, with falsifiable predictions.
> Is it a simple yes or no whether hot water freezes faster? No. Under some conditions, yes. Under others, even the inverse Mpemba effect occurs. 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.