Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower

TL;DR

This paper introduces a CTRW model with finite mean residence times that exhibits transient subdiffusion on large time scales, leading to faster-than-expected transport in biological systems, contrasting traditional models with divergent mean waiting times.

Contribution

It presents an alternative CTRW and FFPE framework with finite mean residence times, showing transient subdiffusion can be faster and does not require long-range correlations.

Findings

Transient subdiffusion occurs on large time scales $ au_c$.

Transport becomes normal for $t o ext{large}$.

Transient subdiffusion is faster than asymptotic normal transport.

Abstract

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale $\tau_c$ which can greatly exceed mean residence time in any trap, $\tau_c\gg <\tau>$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg\tau_c$. However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anti-correlations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because of macroscopic viscosity of cytoplasm is finite.