Persistent luminescence as emergent relaxation in a disordered kinetic landscape

Persistent luminescence is commonly described using discrete trap models or empirical decay laws, which often obscure the distributed nature of the underlying relaxation dynamics and limit direct comparison across materials. Here, a kinetic landscape framework is introduced in which persistent luminescence emerges from relaxation within a disordered ensemble of trapping states described by a continuous density of states. Within the present Gaussian implementation, the decay dynamics are governed by two dimensionless kinetic coordinates: an effective depth parameter (η), associated with the characteristic release timescale, and a disorder parameter (ξ), which quantifies the breadth of escape pathways. Their combined finite-window descriptor, Φ=ηξ, provides a compact representation of the interplay between depth and disorder across distinct relaxation regimes. Decay curves from chemically distinct sulfide, aluminate, silicate, and oxide phosphors collapse onto a reduced kinetic manifold, enabling direct comparison of materials within a common depth–disorder space despite substantial differences in composition and synthesis history. The framework further reveals an internal gauge structure in which variations of the reference attempt frequency shift the representation of η without altering the underlying kinetic organization, leading naturally to gauge-invariant effective timescales. Alternative density-of-states geometries were additionally examined, indicating that the Gaussian representation acts as a minimal centered-disorder implementation while preserving the broader flexibility of the kinetic landscape formalism. Together, these results establish a unified statistical description of persistent luminescence relaxation and provide a transferable framework for interpreting the effects of disorder, composition, and processing on emergent afterglow dynamics.