Kinetic Equations for Diffusion in the Presence of Entropic Barriers
arXiv:cond-mat/0110442 · doi:10.1103/PhysRevE.64.061106
Abstract
We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to the description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.
16 pages, 5 figures. Accepted for publication in Phys. Rev. E
References in corpus (1)
Cited by in corpus (121)
- Fluids at the Nanoscale: from continuum to sub-continuum transport
- Entropic transport: Kinetics, scaling and control mechanisms
- Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria
- Entropic Stochastic Resonance
- Entropic Splitter for Particle Separation
- Rectification in synthetic conical nanopores: a one-dimensional Poisson-Nernst-Planck modeling
- Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
- Current in a three-dimensional periodic tube with unbiased forces
- Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
- Entropic particle transport in periodic channels
- Diffusion with resetting in a logarithmic potential
- Entropic stochastic resonance: the constructive role of the unevenness
- Concentration Polarization and Metal Dendrite Initiation in Isolated Electrolyte Microchannels
- Hydrodynamically enforced entropic trapping of Brownian particles
- Entropic electrokinetics: recirculation, particle separation and negative mobility
- Double Entropic Stochastic Resonance
- Tracer diffusion in crowded narrow channels. Topical review
- Model microswimmers in channels with varying cross section
- Homogeneous Nucleation in Inhomogeneous Media II: Nucleation in a Shear Flow
- Confined Brownian ratchets
- Brownian transport in corrugated channels with inertia
- A channel Brownian pump powered by an unbiased external force
- Driven Brownian transport through arrays of symmetric obstacles
- Biased Brownian motion in extreme corrugated tubes
- Transport of overdamped Brownian particles in a two-dimensional tube: Nonadiabatic regime
- Diffusion of finite-size particles in channels with random walls
- Cooperative rectification in confined Brownian ratchets
- Directed transport driven by the transverse wall vibration
- Effective one-dimensional description of confined diffusion biased by a transverse gravitational force
- Entropic transport - A test bed for the Fick-Jacobs approximation
- Entropically-induced asymmetric passage times of charged tracers across corrugated channels
- Mean-performance of sharp restart I: Statistical roadmap
- Non-monotonous polymer translocation time across corrugated channels: comparison between Fick-Jacobs approximation and numerical simulations
- Geometric stochastic resonance in a double cavity
- Diffusion of finite-size particles in confined geometries
- Resetting transition is governed by an interplay between thermal and potential energy
- Thermal noise can facilitate energy transformation in the presence of entropic barriers
- Thermodynamics and statistical mechanics of chemically-powered synthetic nanomotors
- Optimizing the Performance of the Entropic Splitter for Particle Separation
- Transport of active particles in an open-wedge channel
- Entropic transport of finite size particles
- Thermal ratchet effect in confining geometries
- Local quasi-equilibrium description of slow relaxation systems
- Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
- Homogeneous Nucleation in Inhomogeneous Media I: Nucleation in a Temperature Gradient
- Steering the potential barriers: entropic to energetic
- First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
- Phase shift induces currents in a periodic tube
- Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs
- Generalized Fick Jacobs Approach for describing Adsorption Desorption Kinetics in Irregular Pores under Non Equilibrium Conditions
- How entropy and hydrodynamics cooperate in rectifying particle transport
- Mean first-passage time to a small absorbing target in an elongated planar domain
- Geometry controlled dispersion in periodic corrugated channels
- Diffusion of Colloidal Rods in Corrugated Channels
- Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties
- Inertial effects on rectification and diffusion of active Brownian particles in an asymmetric channel
- Stochastic and Deterministic Vector Chromatography of Suspended Particles in 1D-Periodic Potentials
- Diffusion of interacting particles in a channel with reflection boundary conditions
- Memory effects in nonlinear transport: kinetic equations and ratchet devices
- Entropy facilitated active transport
- Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited
- Diffusion in a Curved Tube
- Rectification and non-Gaussian diffusion in heterogeneous media
- Transport properties of Brownian particles confined to a narrow channel by a periodic potential
- Working under confinement
- Pumping and mixing in active pores
- Driven tracers in narrow channels
- Dispersion in two-dimensional periodic channels with discontinuous profiles
- A Comment on the Scale Length Validity of the Position Dependent Diffusion Coefficient Representation of Structural Heterogeneity
- Active microrheology in corrugated channels
- The probability distribution of Brownian motion in periodic potentials
- Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
- Kinetic theory of a confined quasi-one-dimensional gas of hard disks
- Antiresonant driven systems for particle manipulation
- Transport of Brownian particles in a narrow, slowly-varying serpentine channel
- Entropy production and rectification efficiency in colloids transport along a pulsating channel
- Confined diffusion in a random Lorentz gas environment
- Field-driven tracer diffusion through curved bottlenecks: Fine structure of first passage events
- Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks
- Enhancement of the longitudinal transport by a weakly transversal drive
- Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media
- Brownian particles in periodic potentials: coarse-graining versus fine structure
- Geometric Brownian Information Engine: Essentials for the best performance
- Diffusion and binding of finite-size particles in confined geometries
- Transport and fluctuation-dissipation relations in asymptotic and pre-asymptotic diffusion across channels with variable section
- Interacting Brownian particles exhibiting enhanced rectification in an asymmetric channel
- Self-diffusion in a quasi-two dimensional gas of hard spheres
- Transport of Brownian particles confined to a weakly corrugated channel
- Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation
- Interactions enhance dispersion in fluctuating channels via emergent flows
- Random resetting in search problems
- Active and Passive Transport of Cargo in a Corrugated Channel: A Lattice Model Study
- Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation
- Measurement-Induced Phase Transitions in Informational Active Matter
- First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results
- Active particles in a tube: a generalized entropy potential approach
- Mesoscopic constitutive relations for dilute polymer solutions
- Projecting diffusion along the normal bundle of a plane curve
- Adsorption and desorption in confined geometries: a discrete hopping model
- Nonsteady-state diffusion in two-dimensional periodic channels
- Macrotransport of active particles in periodic channels and fields: rectification and dispersion
- Achievable Information-Energy Exchange in a Brownian Information Engine through Potential Profiling
- Turning catalytically active pores into active pumps
- Thermodynamic basis of the concept of "recombination resistances"
- Local pressure for confined systems
- Splitting probabilities for dynamics in corrugated channels: passive VS active Brownian motion
- Effective diffusion in the region between two surfaces
- Thermodynamically Induced Particle Transport: Order-by-Induction and Entropic Trapping at the Nano-Scale
- Enhanced diffusion in soft-walled channels with a periodically varying curvature
- Collective Transport of Lennard-Jones Particles through One-Dimensional Periodic Potentials
- Enhanced molecular diffusion near a soft fluctuating membrane
- Exact solution to Fick-Jacobs equation
- A new method for measurement and quantification of tracer diffusion in nanoconfined liquids
- Steric modulation of ionic currents in DNA translocation through nanopores
- Conformal quantum mechanics and Fick-Jacobs equation
- Diffusion of gravitactic chiral active Brownian particles in an asymmetric channel
- Scaling regimes for unsteady diffusion across particle-stabilized fluid interfaces
- Mass-based separation of active Brownian particles in an asymmetric channel
- Mean first-passage time to a small absorbing target in three-dimensional elongated domains
- Active transport: A kinetic description based on thermodynamic grounds
- Improving the efficiency of finite-time memory erasure with potential barrier shaping