What do glass beads in water and trapped ions have in common? According to a new theoretical framework, both defy normal thermodynamics in the exact same way.
image from Gemini Imagen 4
The Mpemba effect—where hotter systems can relax to equilibrium faster than cooler ones—has been unified under a single theoretical framework explaining both classical and quantum instances. John Goold's team at Trinity College Dublin treats anomalous relaxation as a resource management problem, where systems with more of a given resource shed it faster than systems with less. This framework bridges previously disparate observations in glass beads, trapped ions, and other systems, building on foundational work by Raz and Lu showing that nonequilibrium systems have access to faster-than-expected trajectories.
Hot water freezes faster than cold water. This is not a typo. The Mpemba effect—named after Tanzanian student Erasto Mpemba, who observed it as a teenager in 1963 and later co-authored a paper on it with physicist Denis Osborne in 1969—has tantalized physicists for decades. The effect is real in certain controlled settings, even if it remains contested for bulk water. But here is the genuinely strange part: physicists have now found that the same counterintuitive logic shows up across classical and quantum systems, in contexts ranging from glass beads in water to trapped ions. And a new theoretical framework claims to explain why.
In a paper published in Physical Review X on March 25, 2026, a team led by John Goold at Trinity College Dublin, with co-authors from Universität zu Köln and Duke University, proposes that both the classical thermal Mpemba effect and its quantum counterparts can be understood as instances of a single underlying principle. The paper, submitted to arXiv in July 2025, treats anomalous relaxation in both domains as a problem of resource management—specifically, how a system with more of a given resource manages to shed it faster than a system with less.
"All these effects you might think of as completely different are actually sort of the same thing," said John Bechhoefer, a physicist at Simon Fraser University, in Science magazine's coverage of the result.
The puzzle has a long history. Mpemba's childhood observation languished as a scientific curiosity until 2017, when Oren Raz at the Weizmann Institute of Science and Zhiyue Lu at the University of North Carolina at Chapel Hill published a mathematical framework explaining the mechanism. Their key insight: systems far from equilibrium have access to a wider variety of possible trajectories toward their final state, and sometimes the longer-looking path is genuinely faster. "Away from equilibrium, your initial intuition completely collapses," Raz told Science.
The first clean experimental confirmation came in 2020, when Bechhoefer's group tracked microscopic glass beads rolling through a hilly underwater landscape and watched the hot beads settle faster than cold ones—verifying the effect in a controlled classical system.
But the story does not end with glass beads. Over the past few years, physicists have discovered the same anomalous relaxation logic in quantum systems. In 2023, Shahaf Aharony Shapira and Yotam Shapira, then a Ph.D. student collaboration at the Weizmann Institute, found the inverse Mpemba effect in single trapped ions: cold ions heated up faster than hot ones. Separately, Sara Murciano at Paris-Saclay University developed a mathematical model showing that quantum systems with more magnetic asymmetry can regain symmetry faster than those with less—a result since confirmed with trapped ions by experimental groups. As Science magazine reported, both teams posted preprints in early 2024, launching a surge of interest in quantum Mpemba effects.
The Goold-Summer paper, published in PRX, attempts to unify these scattered observations under a single formalism. The authors use resource theory—a framework borrowed from quantum information theory—to argue that both the classical thermal Mpemba effect and the quantum symmetry-restoring version are expressions of the same underlying structure. The thermal effect, they argue, arises from the resource theory of athermality: systems with more thermal resource to shed can find shortcut pathways that bring them to equilibrium faster. The quantum symmetry-restoring effect follows from resource theories of asymmetry, using the same logic. Crucially, the Mpemba effect in the symmetry-restoring case is governed by the initial overlap with the slowest symmetry-restoring mode—a quantitative parameter that determines when the effect appears.
The paper goes further. The authors argue that this resource-theoretical lens naturally extends beyond thermal and asymmetry resources to entanglement, magic states, and non-Gaussianity—additional quantum resources that play roles in quantum computation and quantum state preparation. "In principle we know how to reach the special initial conditions," Krissia Zawadzki, a physicist at the São Carlos Institute of Physics, told Science. Her team has already demonstrated the effect in a proof-of-concept quantum Otto refrigerator, showing that harnessing the quantum Mpemba effect could increase cooling power by roughly 10 percent. The team published its experimental results in a preprint in November 2025.
Goold described the framework himself as "one ring to rule them all"—a phrase he borrowed from Tolkien to capture the ambition of unifying disparate phenomena under a single conceptual structure.
There are reasons to be measured about the practical implications. The Goold-Summer paper is theoretical: it provides a unifying language, not a new empirical measurement of cooling power gains. The 10 percent figure comes from Zawadzki's experimental work, a separate research program. Identifying the specific initial conditions that produce Mpemba behavior in any given system remains a non-trivial problem, and engineering those conditions in a real quantum refrigerator is an open challenge. Separately, the classical Mpemba effect in water specifically remains contested in the literature—the history of overclaimed Mpemba results is long enough that the pattern warrants its own skepticism.
That said, the framework is peer-reviewed, open-access, and builds on a coherent set of prior experimental results. For researchers working on quantum thermodynamics, far-from-equilibrium quantum systems, or quantum state engineering, the resource-theory unification provides a map of a territory that was previously charted in fragments. Whether it leads somewhere useful is a question the physics community will answer over the next few years. But for now, the map is in PRX, and it is worth knowing it exists.
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