Generalized Mpemba effect in diffusion-controlled spin-dependent delayed fluorescence

Abstract

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.