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The Mpemba Effect

Can Hot Water Really Freeze Before Cold Water?

Big Question: What exactly must be measured before we can say that a hotter system “cooled” or “froze” faster than a cooler one?

Quick Answer

For ordinary water, the phrase “hot water freezes faster than cold water” hides many experimental choices. Does “freeze” mean first ice crystal, reaching 0 °C, forming a visible skin, or becoming completely solid? Are the samples the same mass? Did the hotter sample lose more water by evaporation? Did convection differ? Did one sample supercool far below 0 °C before nucleating ice?

A careful 2016 Scientific Reports study found no meaningful evidence that otherwise comparable hotter water reliably cools to 0 °C faster than cooler water and emphasised major reproducibility problems in traditional freezing experiments.

But the story did not end there. In 2020, a Nature experiment demonstrated a strong, reproducible Mpemba effect in a controlled colloidal system. Since then, generalized Mpemba effects have become an active area of non-equilibrium statistical physics, including quantum systems.

Nature — Exponentially Faster Cooling in a Colloidal System →

What You Will Learn

• Why “freezes faster” needs a precise operational definition.
• How Newton-style cooling intuition works.
• Why hotter water initially loses heat faster.
• Why that alone does not prove the Mpemba effect.
• How evaporation changes mass and energy loss.
• How convection changes temperature distribution.
• Why dissolved gases and container contact can matter.
• What supercooling and nucleation do to freezing time.
• Why repeated trials are essential.
• How generalized Mpemba effects arise from multiple relaxation modes.
• What the strong Mpemba effect means.
• Why modern Mpemba physics extends far beyond water.

Part 1 — Start With the Simplest Cooling Model

For a small object cooling in a constant-temperature environment, a common approximation is Newton’s law of cooling:

dT/dt = −k(T − T_env)

The hotter sample has a larger temperature difference from the environment, so it loses heat faster initially.

But it also has more thermal energy to lose before reaching the cooler sample’s starting temperature. In this simple one-variable model, the hotter sample cannot overtake the cooler one if everything else is identical.

Part 2 — Real Cooling Water Is Not One Number

A beaker of water has a temperature field, not one perfectly uniform temperature.

Warm water drives stronger buoyant convection. The surface loses heat by evaporation, convection and radiation. The container conducts heat to shelves and air. The freezer thermostat may switch on and off.

Heating the sample can therefore change the subsequent state of the system, not merely its starting thermometer reading.

Part 3 — “Freeze” Has Several Possible Endpoints

Possible endpoint	What it measures
Reach 0 °C	Sensible cooling only
First ice crystal	Nucleation onset
First visible ice	Nucleation plus early growth
50% frozen	Phase-change progression
Completely solid	Cooling plus latent heat plus growth geometry

Two experiments can therefore both claim to study “freezing time” while measuring different physical events.

Part 4 — Evaporation Can Make the Hot Sample Smaller

Hotter water evaporates more rapidly. Escaping molecules carry latent heat away, increasing cooling.

Evaporation also reduces the mass that later needs to cool and freeze.

If a hot sample begins at 100 g but loses several grams while a cold sample does not, the two samples are no longer identical systems.

This can create a perfectly real faster-freezing observation without establishing a universal temperature-only law.

Part 5 — Convection Changes the Route Through Temperature Space

Heating produces stronger density differences within water. Warm water rises and cooler water sinks, setting up convective circulation.

That circulation changes how quickly heat reaches the container walls and surface. It also changes where a thermometer placed at one height reads the local temperature.

The 2016 Scientific Reports analysis showed that measurement position and convection can substantially affect apparent cooling curves.

Scientific Reports — Questioning the Mpemba Effect: Hot Water Does Not Cool More Quickly Than Cold →

Part 6 — Supercooling Makes Freezing a Nucleation Problem

Pure water does not always begin crystallising exactly at 0 °C.

A liquid can cool below its equilibrium freezing point and remain metastable until a suitable ice nucleus forms.

temperature below 0 °C ≠ guaranteed immediate ice formation.

If one sample supercools to −8 °C before nucleating while another nucleates at −2 °C, the second can begin freezing first even if its earlier cooling history was slower.

Part 7 — Nucleation Is Sensitive to Tiny Details

Dust, scratches, container material, dissolved gases, vibration and microscopic ice seeds can alter nucleation probability.

That makes freezing experiments statistically noisy. A single pair of cups is weak evidence because one microscopic nucleation event can reverse the order.

Good experiments need many repetitions and a pre-declared endpoint.

Part 8 — Heating Can Change the Initial State in Hidden Ways

Boiling or strong heating can remove dissolved gases, alter convection patterns, change evaporation history and modify the thermal contact between a container and a frosty freezer shelf.

So two samples with the same current temperature may not be physically identical if one has been heated previously and the other has not.

This is the bridge to modern Mpemba physics: history can matter because temperature may not fully specify the state.

Part 9 — What the 2016 Critique Actually Showed

Burridge and Linden analysed published water-cooling data and performed carefully controlled experiments. Under their operational definition—cooling otherwise comparable water samples to 0 °C—they found no meaningful reproducible Mpemba effect.

They also noted that reports including the freezing process were strongly affected by supercooling and experimental variability.

The correct lesson is not “Mpemba was foolish.” The lesson is that an intriguing observation requires a definition, controls, replication and a mechanism before it becomes a reliable general law.

Part 10 — Then Physics Generalised the Question

Instead of asking only whether hot water freezes first, statistical physicists asked a deeper question:

Can a system prepared farther from equilibrium relax to equilibrium faster than one prepared closer?

In a complex system, relaxation can occur along several modes with different decay rates. The initial state determines how strongly each mode is excited.

A “hotter” initial state can sometimes have very little overlap with the slowest mode, allowing it to bypass the long tail that delays a “cooler” state.

Part 11 — The 2020 Colloidal Experiment Made It Reproducible

Kumar and Bechhoefer engineered a tiny colloidal particle in a controlled energy landscape. They prepared different effective initial temperatures, quenched the system to the same bath and measured relaxation.

They observed the hotter preparation relaxing exponentially faster than a cooler preparation under carefully selected conditions, quantitatively matching theory.

This was not water freezing. It was a clean demonstration that Mpemba-type anomalous relaxation is a genuine phenomenon in non-equilibrium statistical mechanics.

Part 12 — What Is the Strong Mpemba Effect?

Near equilibrium, a system’s slowest relaxation mode usually dominates at long times.

If an initial state can be prepared so that its projection onto that slow mode is zero or extremely small, the system relaxes through faster modes instead.

remove the slow mode → relaxation can accelerate dramatically.

This is called a strong Mpemba effect.

Part 13 — Mpemba Physics Now Reaches Quantum Systems

Recent experiments and theory have identified quantum analogues in which a state that begins farther from the target equilibrium or symmetry condition relaxes faster than a closer state.

A 2025 Nature Reviews Physics perspective surveys several quantum Mpemba effects and the role of fluctuations, symmetry and integrability.

Nature Reviews Physics — The Quantum Mpemba Effects →

This modern work does not retroactively prove every claim about cups of water. It shows that the deeper mathematical phenomenon is much broader than the original kitchen story.

Part 14 — Even Water Remains an Active Modelling Problem

In 2025, molecular simulations reported Mpemba-like freezing inversions in model water and simpler Lennard-Jones systems, linking the effect in the water model to how long different initial states remain metastable before crystallisation.

Communications Physics — Simulations of Mpemba Effect in Water and Lennard-Jones Models →

Simulation evidence is valuable because variables can be controlled precisely, but it is not the same as demonstrating that household hot water will reproducibly beat household cold water in a freezer.

Part 15 — Follow One Proper Mpemba Experiment

1. Define exactly what “finish” means.
2. Use identical containers and measured masses.
3. Control or measure evaporation.
4. Record environmental temperature continuously.
5. Use several thermometers or justify measurement position.
6. Record the complete cooling curve.
7. Detect nucleation separately from reaching 0 °C.
8. Measure remaining mass after cooling.
9. Repeat many trials at each initial condition.
10. Quantify uncertainty and trial-to-trial variation.
11. Test proposed mechanisms by changing one factor at a time.
12. Only then ask whether an inversion is reproducible and statistically meaningful.

Think Like a Scientist: What Would Count as Convincing Evidence?

• A precise definition of the relaxation endpoint.
• Many repeated trials.
• Randomised order of runs.
• Controlled sample mass and geometry.
• Measured evaporation.
• Separate measurement of cooling and nucleation.
• Statistical confidence intervals.
• A mechanism that predicts when the inversion should appear and disappear.
• Replication by independent laboratories.

Observation vs Inference

• Historical observation: particular hotter samples have sometimes appeared to freeze before cooler samples.
• Controlled water evidence: a universal, repeatable “hot water freezes faster” law is not supported.
• Controlled non-equilibrium evidence: reproducible generalized Mpemba effects occur in designed classical systems.
• Modern extension: Mpemba-like anomalous relaxation has theoretical and experimental quantum forms.
• Boundary: evidence for the generalized phenomenon must not be used to claim every household water-freezing anecdote is the same effect.

Common Misconceptions and Better Models

Misconception	Better model
Hot water always freezes faster than cold water.	No universal rule exists; results depend on definition, preparation and conditions.
If hot water cools faster initially, it must finish first.	A larger initial heat-loss rate does not by itself overcome the hotter sample’s larger energy content.
Reaching 0 °C means freezing has begun.	Water can supercool below 0 °C before nucleating ice.
One freezer experiment proves the effect.	Nucleation and freezer conditions are variable; repeated controlled trials are essential.
The 2016 criticism means all Mpemba physics is false.	Generalized Mpemba relaxation has since been demonstrated reproducibly in controlled systems.
Modern quantum Mpemba effects prove the household-water claim.	They show a broader relaxation principle, not equivalence of every mechanism.

Checkpoint Questions

1. Why is “freezes faster” scientifically ambiguous?
2. Why does a hotter sample initially lose heat faster?
3. Why does that not prove it reaches the endpoint first?
4. How can evaporation change the comparison?
5. What is supercooling?
6. Why does nucleation create experimental variability?
7. What did the 2016 study conclude under its definition?
8. What was demonstrated in the 2020 colloidal experiment?
9. What is a strong Mpemba effect?
10. Why is the modern generalized effect not identical to the kitchen-water claim?

Answer Key

Open after attempting the questions

1. It may refer to reaching 0 °C, nucleating ice, forming some ice or becoming fully solid.
2. The temperature difference to the cold environment is larger.
3. It also begins with more energy to lose and the full cooling dynamics matter.
4. It removes both mass and latent heat, changing the system being compared.
5. Liquid water remaining unfrozen below its equilibrium freezing point.
6. Microscopic seeds and container conditions can strongly change when ice first forms.
7. No meaningful reproducible inversion for otherwise comparable water cooling to 0 °C.
8. A controlled system prepared hotter could reproducibly relax much faster to equilibrium.
9. A preparation that nearly eliminates the slowest relaxation mode.
10. Different systems can share anomalous relaxation mathematics while using different microscopic mechanisms.

Primary Science Bridge

• hotter objects can lose heat faster initially;
• freezing is a phase change;
• evaporation removes water and energy;
• experiments must keep variables controlled;
• one surprising result should be repeated before becoming a rule.

Secondary and JC Bridge

Core idea	Higher-resolution route
Cooling	Newtonian and non-Newtonian heat transfer
Convection	Rayleigh-number-dependent flow
Evaporation	Latent heat and mass loss
Freezing	Nucleation and metastability
Data	Repeated trials and uncertainty
Statistical physics	Relaxation eigenmodes and non-equilibrium state space

Deep Science Window — Temperature Does Not Fully Describe a Non-Equilibrium State

At equilibrium, temperature can summarise enormous microscopic complexity. Away from equilibrium, two systems with the same average temperature can have different spatial distributions, correlations, concentrations or occupation probabilities. Those hidden state variables can change the route and timescale of relaxation.

Deep Science Window — Relaxation Modes

A complex system returning to equilibrium can often be decomposed into modes that decay at different rates. The slowest mode dominates long-time relaxation unless the initial state has little or no projection onto it. That gives a general mathematical route for a farther initial state to arrive sooner.

Evidence Boundaries

• Mpemba effect ≠ hot water always freezes faster.
• Higher initial heat flux ≠ guaranteed earlier finish.
• 0 °C ≠ automatic ice nucleation.
• One trial ≠ reproducible phenomenon.
• Generalized Mpemba effect ≠ one universal microscopic mechanism.
• Simulation or quantum evidence ≠ proof of every household freezing claim.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW: cooling rate, evaporation, convection, supercooling, nucleation, relaxation mode.

CONNECT: experimental preparation to hidden state variables, hidden variables to relaxation path, and relaxation path to finishing time.

EXPLAIN: why a farther-from-equilibrium state can sometimes relax faster without violating thermodynamics.

APPLY: design a freezing experiment that separates cooling, nucleation and complete solidification.

CHECK: demand a precise endpoint and repeated evidence whenever someone says “hot water freezes faster.”

Research Sources and Further Reading

• Scientific Reports — Questioning the Mpemba Effect: Hot Water Does Not Cool More Quickly Than Cold
• Nature — Exponentially Faster Cooling in a Colloidal System
• Nature Reviews Physics — A Fresh Understanding of the Mpemba Effect
• Communications Physics — Simulations of Mpemba Effect in Water and Lennard-Jones Models
• Nature Reviews Physics — The Quantum Mpemba Effects