Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities

Abstract

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, that can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.

19 pages, 6 figures, RevTeX. Physical Review X, at press

References in corpus (12)

• Anomalous transport in the crowded world of biological cells
• Universal nature of particle displacements close to glass and jamming transitions
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Diffusion and mixing in gravity-driven dense granular flows
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Brownian motion with dry friction: Fokker-Planck approach
• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories
• Tracer diffusion in a sea of polymers with binding zones: mobile vs frozen traps
• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk

Cited by in corpus (166)

• Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Diffusion-limited reactions in dynamic heterogeneous media
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution
• Spectral content of a single non-Brownian trajectory
• Paradigm shift in diffusion-mediated surface phenomena
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• A model of non-Gaussian diffusion in heterogeneous media
• First-passage and first-hitting times of Levy flights and Levy walks
• Two Coupled Mechanisms Produce Fickian, yet non-Gaussian Diffusion in Heterogeneous Media
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Analytic approaches of the anomalous diffusion: a review
• Generalised geometric Brownian motion: Theory and applications to option pricing
• First passage statistics for diffusing diffusivity
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
• The Hitchhiker model for Laplace diffusion processes in the cell environment
• Heterogeneities Shape Passive Intracellular Transport
• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Wind Power Persistence Characterized by Superstatistics
• Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity
• Fractional Brownian motion with a reflecting wall
• Universal Transport Dynamics of Complex Fluids
• Superstatistical approach to air pollution statistics
• Time-averaged MSD for switching diffusion
• On relation between generalized diffusion equations and subordination schemes
• Universal spectral features of different classes of random diffusivity processes
• Physically consistent numerical solver for time-dependent Fokker-Planck equations
• Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise
• Mutual information disentangles interactions from changing environments
• Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation
• Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
• Length scales in Brownian yet non-Gaussian dynamics
• Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics
• Non-Gaussianity of van Hove Function and Dynamic Heterogeneity Length Scale
• Chloroplasts in plant cells show active glassy behavior under low light conditions
• Superstatistical modelling of protein diffusion dynamics in bacteria
• A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models
• Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
• Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
• Non-Gaussian diffusion in static disordered media
• Lévy-walk-like Langevin dynamics
• Non-Gaussian diffusion of mixed origins
• Controlling particle currents with evaporation and resetting from an interval
• Is Fickian Yet Non-Gaussian Diffusion Ubiquitous?
• Codifference can detect ergodicity breaking and non-Gaussianity
• Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
• Non-Gaussian diffusion near surfaces
• Fractional Fokker-Planck equation from non-singular kernel operators
• Information propagation in multilayer systems with higher-order interactions across timescales
• Non-Gaussian Normal Diffusion in a Fluctuating Corrugated Channel
• Non-Gaussian displacements in active transport on a carpet of motile cells
• Exact extreme, order and sum statistics in a class of strongly correlated system
• Convergence to a Gaussian by narrowing of central peak in Brownian yet non-Gaussian diffusion in disordered environments
• Robust random search with scale-free stochastic resetting
• Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics
• Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit
• Anomalous dynamical scaling determines universal critical singularities
• Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor
• Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search
• Polymers critical point originates Brownian non-Gaussian diffusion
• Non-Gaussian anomalous dynamics in systems of interacting run-and-tumble particles
• Large Deviation in Continuous Time Random Walks
• Statistics of diffusive encounters with a small target: Three complementary approaches
• Anomalous diffusion originated by two Markovian hopping-trap mechanisms
• Stochastic Inference of Surface-Induced Effects using Brownian Motion
• Analyzing Spatio-Temporal Dynamics of Dissolved Oxygen for the River Thames using Superstatistical Methods and Machine Learning
• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• First-passage times to anisotropic partially reactive targets
• Scattering fingerprints of two-state dynamics
• Ergodic property of random diffusivity system with trapping events
• Mittag-Leffler functions in superstatistics
• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Hidden Order Beyond Hyperuniformity in Critical Absorbing States
• Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity
• Integral decomposition for the solutions of the generalized Cattaneo equation
• Anomalous Fluctuations of Extremes in Many-Particle Diffusion
• Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches
• Superstatistical approach of the anomalous exponent for scaled Brownian motion
• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
• Tracer Diffusion on a Crowded Random Manhattan Lattice
• Exact first-passage time distributions for three random diffusivity models
• Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity
• Encounter-based approach to diffusion with resetting
• Spatio-temporal complexity of power-grid frequency fluctuations
• Fickian yet non-Gaussian diffusion in two-dimensional Yukawa liquids
• Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets
• Fractional Brownian motion with fluctuating diffusivities
• Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior
• Generalization of Stokes-Einstein relation to coordinate dependent damping and diffusivity: An apparent conflict
• Diffusion Transients in Motility-Induced Phase Separation
• Multifractional Brownian motion with telegraphic, stochastically varying exponent
• Anomalous Diffusion: Fractional Brownian Motion vs. Fractional Ito Motion
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition
• Reversible reactions controlled by surface diffusion on a sphere
• Transport and phase separation of active Brownian particles in fluctuating environments
• A Comment on the Scale Length Validity of the Position Dependent Diffusion Coefficient Representation of Structural Heterogeneity
• Different glassy characteristics are related to either caging or dynamical heterogeneity
• Brownian non-Gaussian diffusion of self-avoiding walks
• Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
• Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: Solution, stochastic paths, and applications
• Mesoscopic Modeling of Random Walk and Reactions in Crowded Media
• Being heterogeneous is disadvantageous: Brownian non-Gaussian searches
• Temperature and friction fluctuations inside a harmonic potential
• Resetting by rescaling: exact results for a diffusing particle in one-dimension
• On superstatistics of energy for a free quantum Brownian particle
• Giant oscillations of diffusion in ac-driven periodic systems
• Non-Gaussian behavior of reflected fractional Brownian motion
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism
• Fluctuating Diffusivity Emerges even in Binary Gas Mixtures
• From continuous-time random walks to controlled-diffusion reaction
• When bigger is faster: a self-van Hove analysis of the enhanced self-diffusion of non-commensurate guest particles in smectics
• Active gels, heavy tails, and the cytoskeleton
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• Are supercooled liquids Fickian yet non Gaussian?
• Superstatistics with cut-off tails for financial time series
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Gas Diffusion in Cement Pastes: An Analysis using a Fluctuating Diffusivity Model
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Random diffusivity processes in an external force field
• Colossal Brownian yet non-Gaussian diffusion in a periodic potential: impact of nonequilibrium noise amplitude statistics
• Efficient $d$-dimensional molecular dynamics simulations for studies of the glass-jamming transition
• Velocity multistability vs ergodicity breaking in a biased periodic potential
• Brownian Yet Non-Gaussian Diffusion of a Light Particle in Heavy Gas: Lorentz Gas Based Analysis
• Hidden Markov modeling of single particle diffusion with stochastic tethering
• First passage time for $g$--subdiffusion process of vanishing particles
• Unravelling Heterogeneous Transport of Endosomes
• Intrinsic cell-to-cell variance from experimental single-cell motility data
• Dynamically emergent correlations in a Brownian gas with diffusing diffusivity
• The Advantage of Foraging Myopically
• Nonequilibrium steady state of Brownian motion in an intermittent potential
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Simulation of the continuous-time random walk using subordination schemes
• Polymer Concentration Regimes from Fractional Microrheology
• Stochastic differential equations driven by deterministic chaotic maps: analytic solutions of the Perron-Frobenius equation
• Conditional entropic approach to nonequilibrium complex systems with weak fluctuation correlation
• Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity
• Hyperphosphorylation-Induced Phase Transition in Vesicle Delivery Dynamics of Motor Proteins in Neuronal Cells
• Reconstruction of substrate's diffusion landscape by the wavelet analysis of single particle diffusion tracks
• Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity
• Diffusion with a broad class of stochastic diffusion coefficients
• Exactly solvable diffusions from space-time transformations
• Non-scaling displacement distributions as may be seen in fluorescence correlation spectroscopy
• First passage time for superstatistical Fokker-Planck models
• Two-states Brownian particle in a Harmonic Potential
• Time-correlated forces and biological variability in cell motility
• yupi: Generation, Tracking and Analysis of Trajectory data in Python
• An empirical method to characterize displacement distribution functions for anomalous and transient diffusion
• Evaluating Gaussianity of heterogeneous fractional Brownian motion
• Unravelling the Flow of Information in a Nonequilibrium Process in the Presence of Hydrodynamic Interactions
• Understanding Brownian yet non-Gaussian diffusion via long-range molecular interactions
• Anomalous dynamics in tracer-particle motions in an electrohydrodynamically driven oil-in-oil system
• Random diffusivity scenarios behind anomalous non-Gaussian diffusion
• Unifying description of the damping regimes of a stochastic particle in a periodic potential
• Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion
• Inertial dynamics of an active Brownian particle
• First passage time properties of diffusion with a broad class of stochastic diffusion coefficients
• Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems
• Non-Gaussian Normal Diffusion in Low Dimensional Systems
• The impact of a random metric upon a diffusing particle
• Stochastic kinetics under combined action of two noise sources
• On the thermodynamic analogy of intracellular diffusivity fluctuations
• Shape-specific fluctuations of an active colloidal interface
• Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities