A glass of hot tea sometimes cools faster than a glass of warm tea. This paradox, known as the Mpemba effect, was long considered a curiosity from the world of liquids. But physicists have found it where no one expected: in the faint glow of organic films placed in a magnetic field.
Molecules in such films can store light energy in dark 'spin' states — triplets (long-lived excited forms with a special magnetic moment). When two triplets meet, they fuse and emit a single bright flash. The magnetic field interferes with this dance: it changes the probabilities of encounters, making some pairs fuse faster and others slower. As a result, the decay curves of luminescence, recorded at different field strengths, cross. A weak field initially quenches the light more quickly but then lags behind; a strong field does the opposite. This is the generalized Mpemba effect: a more 'excited' system calms down earlier than one that started closer to rest.
The authors derived a simple criterion: if the product of the characteristic time of the fast decay and the amplitude of the slow tail for one field is smaller than for another, expect a crossing. Interestingly, the finale is always the same — complete darkness when all triplets have vanished. The magnetic field merely redistributes the routes to this finale, without changing the destination. The work links the oddities of spin photochemistry with the modern view of the Mpemba effect, where what matters is not temperatures but the very possibility of overtaking on the path to equilibrium.
as written by the authors arXiv:2606.21003
The Mpemba effect is commonly associated with anomalous thermal relaxation, in which a system prepared at a higher temperature reaches equilibrium faster than one prepared at a lower temperature. In modern formulations, however, its defining feature is broader: a state initially farther from equilibrium can relax faster than a closer one, or, equivalently, relaxation trajectories can cross. Here, we show that magnetic-field-dependent delayed fluorescence in triplet-fusion systems realizes a generalized Mpemba effect driven by external control of spin-selective kinetics. Using a diffusion-controlled geminate-recombination extension of the Johnson--Merrifield model, we demonstrate that delayed-fluorescence trajectories obtained at different magnetic fields cross when geminate fusion is effective. We further derive a compact kinetic criterion for such crossing in terms of the competition between intermediate-time decay rates and long-time power-law amplitudes. This criterion captures the interplay between effective fast and slow relaxation contributions. Within this kinetic framework, the final state is independent of the external control parameter and is defined as the fully relaxed state in which no separated triplet population remains. The generalized Mpemba effect therefore arises from the redistribution of transient relaxation pathways associated with geminate recombination, whereas bulk diffusion-controlled processes contribute only to the final relaxation. These results link anomalous relaxation in spin-dependent photokinetics to modern formulations of the generalized Mpemba effect and show how trajectory crossing can emerge in systems governed by diffusion-controlled geminate recombination and non-Markovian kinetics.
The Mpemba effect is named after a Tanzanian schoolboy who, in 1963, noticed that hot ice cream freezes faster than warm ice cream and pestered his teachers with questions until physicists acknowledged he was right.
In Kurt Vonnegut's novel 'Cat's Cradle', there is ice-nine, capable of instantly freezing water at room temperature — a fantastic inversion of the Mpemba effect, where equilibrium is reached by a leap rather than gradual cooling.