Scaling law for subdiffusive-to-diffusive transition time in heterogeneous nonequilibrium systems

The transition from subdiffusion to normal diffusion is ubiquitous in complex systems, with experimentally observed transition times spanning several orders of magnitude. However, a scaling law governing the transition time remains unclear. To address this issue, we introduce an analytically tractable model that exhibits a unified subdiffusive-to-diffusive transition, in which tracer particles diffuse in a heterogeneous landscape under Ornstein-Uhlenbeck driving. From this model, we find a scaling law for the transition time, t_{T}≃f(α,K_{0},L)D_{e}(D,τ)^{1/α-1}. Here, the prefactor f depends on the intrinsic system parameters (the subdiffusion exponent α, diffusion coefficient K_{0}, and characteristic length L), while D_{e} denotes an effective driving strength determined by the driving correlation strength D and correlation time τ. Experimental data from diverse complex systems support this scaling law, providing a predictive framework for subdiffusive-to-diffusive transition times across a wide range of scales.