Being heterogeneous is disadvantageous: Brownian non-Gaussian searches

Abstract

Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.

References in corpus (9)

• The large deviation approach to statistical mechanics
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• Non-Gaussian diffusion near surfaces
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• Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit
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Cited by in corpus (7)

• Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Observation-Time-Induced Crossover from Fluctuating Diffusivity
• Two-states Brownian particle in a Harmonic Potential
• Rare Events and Redundancy in Random Walkers Target Search in a Finite Domain
• First passage time properties of diffusion with a broad class of stochastic diffusion coefficients
• Decoupling of single-particle and collective dynamics in arrested phase-separating glassy mixtures