The Mpemba Effect: When Hot Water Freezes First

A schoolboy's ice cream and a 2,000-year-old puzzle

The effect carries the name of Erasto B. Mpemba, who in 1963 was a secondary-school student in Tanzania making ice cream. Told to boil his milk-and-sugar mix and let it cool before freezing, he instead put it in the freezer while still hot — and found it froze before a classmate's cooled mixture. His teacher dismissed it as "Mpemba's physics." When physicist Denis G. Osborne visited his school, Mpemba pressed the question; Osborne ran the experiment, confirmed the anomaly, and the two published "Cool?" in Physics Education in 1969, reporting that beakers starting near 90–100 °C sometimes froze ahead of beakers starting near 35 °C.

The observation is far older. Aristotle noted in the Meteorologica that people warmed water to cool it faster, and Francis Bacon and René Descartes both remarked on it in the 1600s. What Mpemba's story added was insistence that a well-mixed, everyday effect deserved a real explanation — and physicists have argued about that explanation ever since.

Why it should be impossible: Newton's law of cooling

The naive objection is powerful. Model the water as a single lumped mass at temperature T losing heat to an environment at T_a. Newton's law of cooling gives

C dT/dt = −hA(T − T_a),  so  T(t) = T_a + (T₀ − T_a) e^−t/τ, with time constant τ = C/(hA).

Two samples that differ only in their starting temperature T₀ follow the same exponential curve; the hotter one is simply further up it, and must reach any target temperature (including 0 °C) later. Under this idealization the Mpemba effect is strictly forbidden. That is the crux: for hot to win, the cooling must not depend on temperature alone. The sample's internal state — its mass, dissolved-gas content, convection pattern, container contact, and nucleation history — must change along the way, so that the two beakers are no longer the same system tracing the same path. Every serious explanation is really a claim about which of these path-dependent variables matters.

Evaporation: losing mass and latent heat

The most quantitatively defensible mechanism is evaporation. Because a liquid's saturation vapor pressure rises roughly exponentially with temperature (the Clausius–Clapeyron relation), water near boiling evaporates dramatically faster than water at room temperature. Evaporation attacks the freezing time on two fronts.

• Less mass to freeze. Ice-cold water still needs its full latent heat of fusion, L_f ≈ 334 kJ/kg, removed. If the hot sample sheds even 2–3% of its mass as vapor, that is 2–3% less water to cool and to freeze.
• Evaporative cooling. Each kilogram that leaves carries away the latent heat of vaporization, L_v ≈ 2.26–2.45 MJ/kg — about seven times the heat of fusion. Losing 2% of a 1 kg sample removes roughly 45 kJ, comparable to cooling the remaining water by about 11 K on its own.

In open beakers this is large and real; it is why hot-water Mpemba reports are easiest to get in wide, uncovered vessels and vanish when the containers are sealed. It is not the whole story, though: careful trials with lids, where mass loss is negligible, sometimes still show the anomaly.

Convection, dissolved gas, and the container

Several coupled effects can bend the cooling curve away from a simple exponential. Hot water sustains vigorous convection: buoyancy from the temperature gradient drives circulation (set by the dimensionless Rayleigh number), continually delivering warm liquid to the surface. That keeps the top hotter than a purely conductive profile would, and since radiative loss scales as T⁴ (Stefan–Boltzmann) and evaporation rises steeply with surface temperature, the hot sample can shed heat faster than its bulk temperature alone suggests.

Two more container-scale effects appear repeatedly. First, frost and thermal contact: a hot beaker set on a freezer's frost layer melts the frost beneath it, then refreezes into direct, high-conductivity contact with the cold shelf, while the cold beaker sits on an insulating frost cushion. Second, dissolved gas and solutes: gas solubility falls as water is heated, so boiled water is degassed, which changes its density profile, convection, and nucleation behavior. Conversely, physicist Jonathan Katz argued that the cold sample retains dissolved carbonates that, as it cools and concentrates, depress its own freezing point — slowing it down rather than speeding the hot one up.

Supercooling and nucleation: the freezing lottery

Freezing is not automatic at 0 °C. Pure water is happy to remain liquid well below it — a metastable supercooled state — because forming the first stable ice crystal requires surmounting a nucleation barrier. On clean water, homogeneous nucleation only becomes inevitable near −38 to −40 °C; in practice, heterogeneous nucleation on dust, container walls, or gas bubbles triggers freezing much earlier, at a temperature that is essentially random from run to run.

In 1995 David Auerbach proposed that this randomness is central: if previously hot samples tend to supercool less (because boiling removes nucleation-suppressing dissolved gas, or seeds crystals differently), they can begin freezing at a higher temperature and thus reach a solid state sooner. This also exposes a definitional trap that has dogged the field: does "freezing time" mean the first appearance of ice, the moment the bulk hits 0 °C, or the instant the sample is solid throughout? Different definitions can reverse which beaker "wins," and the stochastic nucleation scatter can swamp any systematic difference.

The modern view: shortcuts through state space

The deepest recent progress abandons water entirely and asks a cleaner question: can a system that starts farther from equilibrium relax to a cold state faster than one that starts closer? In 2017 Zhiyue Lu and Oren Raz answered yes, using a general Markovian (master-equation) description of relaxation. Approach to equilibrium is a sum of decaying eigenmodes; the slowest mode dominates the tail, weighted by an overlap coefficient a₂ that depends on the initial condition. If a₂ is non-monotonic in starting temperature, a hotter start can carry less of the slow mode and overtake a cooler one. When a₂ vanishes exactly, the slow mode is skipped altogether — the strong Mpemba effect, with exponentially faster relaxation — and the same math predicts an inverse effect, where a cold system heats up faster.

In 2020 Avinash Kumar and John Bechhoefer at Simon Fraser University turned this into a clean experiment. Using a feedback (electrokinetic) trap, they held a single micron-scale colloidal bead in a sculpted double-well potential, its dynamics governed by the Fokker–Planck equation, and directly observed both the Mpemba and the exponentially faster strong-Mpemba relaxation. The picture generalizes far beyond a beaker: Mpemba-like anomalies have since been reported in granular gases, spin systems, clathrate hydrates, and, in 2024, quantum analogues in trapped-ion platforms.

Is it even real? The reproducibility debate

Honesty requires flagging the controversy. In 2016 Henry Burridge and Paul Linden published "Questioning the Mpemba effect," reporting that in carefully controlled trials hot water did not reliably freeze first, and arguing that the effect is so sensitive to definition and setup that it is not a robust, well-posed phenomenon for bulk water. Their point is not that the historical observations were faked, but that the cooling of an open beaker is a messy tangle of evaporation, convection, nucleation, and container contact whose outcome flips with small changes — exactly the ingredients that make it hard to reproduce.

So the modern verdict is layered. In idealized, controlled model systems, an Mpemba-type effect is now a rigorously established feature of nonequilibrium relaxation. In a literal beaker of water, whether hot beats cold depends on a delicate, sometimes irreproducible balance of the mechanisms above. The lasting value is conceptual: the effect is a vivid reminder that a system's path through state space, not just its instantaneous temperature, sets how fast it reaches equilibrium — a principle now being explored to design faster cooling, quenching, and material-processing protocols.

Leading proposed mechanisms for the Mpemba effect and their current status

Mechanism	Physical basis	Predicted advantage for hot water	Status / caveat
Evaporation	Clausius–Clapeyron vapor pressure; latent heat of vaporization	Loses a few % of mass, so less to freeze, plus strong evaporative cooling	Real and large in open beakers; suppressed in sealed / lidded ones
Convection	Buoyancy-driven currents (Rayleigh number)	Vigorous stirring keeps the top hot, boosting radiative and evaporative loss	Plausible; sensitive to geometry and volume
Dissolved gas / solutes	Gas solubility falls with temperature; solute freezing-point depression	Degassed hot water may nucleate ice differently; cold water's solutes lower its freezing point	Debated; effect size uncertain
Supercooling & nucleation	Metastable liquid below 0 °C; stochastic nucleation	Previously hot water may supercool less and nucleate sooner	Real but random; a major source of irreproducibility
Relaxation shortcut	Master / Fokker–Planck eigenmode overlap	A hot start can take a faster path through state space to the cold state	Rigorously demonstrated in model systems (2017–2020)