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, $t_{\text{T}}\simeq f(\alpha ,K_0,L)D_{\text{e}}{(D,\tau )}^{\frac{1}{\alpha -1}}$. Here, the prefactor $f$ depends on the intrinsic system parameters (the subdiffusion exponent $\alpha$, diffusion coefficient $K_0$, and characteristic length $L$), while $D_{\text{e}}$ denotes an effective driving strength determined by the driving correlation strength $D$ and correlation time $\tau$. 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.

Close

PrevNext

View figure in article

• Classical statistical mechanics
• Diffusion
• Noise-induced transitions
• Nonequilibrium statistical mechanics