Random diffusivity processes in an external force field

Abstract

Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this paper studies the effect of an external force acting on two kinds of random diffusivity models whose difference is embodied in whether the fluctuation-dissipation theorem is valid. Based on the two random diffusivity models, we derive the Fokker-Planck equations with an arbitrary external force, and analyse various observables in the case with a constant force, including the Einstein relation, the moments, the kurtosis, and the asymptotic behaviors of the probability density function of particle's displacement at different time scales. Both the theoretical results and numerical simulations of these observables show significant difference between the two kinds of random diffusivity models, which implies the important role of the fluctuation-dissipation theorem in random diffusivity systems.

arXiv comment12 pages, 4 figures

References in corpus (33)

• Superstatistics
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Dynamical foundations of nonextensive statistical mechanics
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Langevin equations for continuous time Lévy flights
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• From non-Brownian Functionals to a Fractional Schrödinger Equation
• Generalized Fokker-Planck equation: Derivation and exact solutions
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Superstatistical Brownian motion
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Ultra-Slow Vacancy-Mediated Tracer Diffusion in Two Dimensions: The Einstein Relation Verified
• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Universal spectral features of different classes of random diffusivity processes
• Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
• Anomalous processes with general waiting times: functionals and multi-point structure
• Large deviations for continuous time random walks
• Lévy-walk-like Langevin dynamics
• Subdiffusion in an external force field
• Ergodic properties of heterogeneous diffusion processes in a potential well
• Sub-diffusion in External Potential: Anomalous hiding behind Normal
• Weak Galilean invariance as a selection principle for coarse-grained diffusive models
• A no-go theorem for ergodicity and an Einstein relation
• Feynman-Kac equation for anomalous processes with space- and time-dependent forces
• Feynman-Kac equation revisited
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Ergodic property of random diffusivity system with trapping events
• Exact first-passage time distributions for three random diffusivity models
• Langevin picture of Lévy walk in a constant force field
• Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters