Universality and ambiguity in extremes of anomalous diffusion

Area of Science:

• Biophysics
• Statistical Mechanics
• Physical Chemistry

Background:

• Many biophysical processes rely on the fastest searcher locating a target among many.
• The fastest first passage time (fFPT) is crucial for understanding search dynamics.
• Previous models with unbounded speeds raised questions about real-world applicability.

Purpose of the Study:

• To investigate fFPTs across diverse diffusion models with bounded and unbounded speeds.
• To determine the universality and limitations of fFPT behavior in physical systems.
• To clarify the impact of anomalous diffusion on search efficiency.

Main Methods:

• Analysis of scaled Brownian motion, Riemann-Liouville fractional Brownian motion, and fractional Brownian motion.
• Mathematical derivations for fFPT in models with bounded and unbounded speeds.
• Comparison of subdiffusive, normal diffusive, and superdiffusive search strategies.

Main Results:

• fFPT decays logarithmically with the number of searchers across all studied models.
• Subdiffusion can be faster than normal diffusion, while superdiffusion can be slower.
• Features (i) and (ii) regarding fFPT behavior are shown to be broadly universal.
• The validity of these features depends on specific model parameters, introducing model-specific ambiguities.

Conclusions:

• The logarithmic decay of fFPT and the potential speed advantage of subdiffusion are universal phenomena in search processes.
• While general trends hold, specific physical system relevance requires careful consideration of individual model dynamics and parameter regimes.
• This work bridges theoretical models of diffusion with the practical constraints of bounded searcher speeds in biophysical contexts.