Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs

Abstract

We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman's ratchet and pawl. Using ideas of the Fick-Jacobs approximation we derive the mean velocity of the particle, the effective diffusion coefficient, and the stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.

References in corpus (48)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Brownian motors: noisy transport far from equilibrium
• The large deviation approach to statistical mechanics
• Steady State Thermodynamics of Langevin Systems
• Kinetic Equations for Diffusion in the Presence of Entropic Barriers
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Entropic Splitter for Particle Separation
• On the heat flux and entropy produced by thermal fluctuations
• Exact microscopic analysis of a thermal Brownian motor
• Work fluctuations for a Brownian particle between two thermostats
• Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
• Excluded-volume effects in the diffusion of hard spheres
• Inattainability of Carnot efficiency in the Brownian heat engine
• Feynman's ratchet and pawl: an exactly solvable model
• Two-temperature Langevin dynamics in a parabolic potential
• An expression for stationary distribution in nonequilibrium steady state
• Hydrodynamically enforced entropic trapping of Brownian particles
• Heat Flow and Efficiency in a Microscopic Engine
• Confined Brownian ratchets
• Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
• Biased Brownian motion in extreme corrugated tubes
• Diffusion of finite-size particles in channels with random walls
• Cooperative rectification in confined Brownian ratchets
• Energetics of a simple microscopic heat engine
• Bound particle coupled to two thermostats
• A heat pump at a molecular scale controlled by a mechanical force
• 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
• Diffusion of finite-size particles in confined geometries
• Photoelectric converters with quantum coherence
• Steering the potential barriers: entropic to energetic
• Heat Fluctuations in Brownian Transducers
• Symmetries of the ratchet current
• How entropy and hydrodynamics cooperate in rectifying particle transport
• Impact of inertia on biased Brownian transport in confined geometries
• Interaction of molecular motors can enhance their efficiency
• Transport properties of Brownian particles confined to a narrow channel by a periodic potential
• Pumping single-file colloids: Absence of current reversal
• Tunable diffusion of magnetic particles in a quasi-one-dimensional channel
• Hidden heat transfer in equilibrium states implies directed motion in nonequilibrium states
• Survival of interacting Brownian particles in crowded 1D environment
• Tracer dynamics in a single-file system with absorbing boundary
• Transport of Brownian particles in a narrow, slowly-varying serpentine channel
• Interacting molecular motors: Efficiency and work fluctuations
• On the transport of interacting particles in a chain of cavities: Description through a modified Fick-Jacobs equation
• Transport and fluctuation-dissipation relations in asymptotic and pre-asymptotic diffusion across channels with variable section
• An oriented process induced by dynamically regulated energy barriers

Cited by in corpus (16)

• Active Brownian Heat Engines
• Physically consistent numerical solver for time-dependent Fokker-Planck equations
• Fluctuations in heat engines
• Two-temperature Brownian dynamics of a particle in a confining potential
• Thermal ratchet effect in confining geometries
• Solitons in overdamped Brownian dynamics
• Autonomous Brownian gyrators: a study on gyrating characteristics
• Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon
• Energetics of a driven Brownian harmonic oscillator
• Force-Free and Autonomous Active Brownian Ratchets
• Mechanochemical Active Ratchet
• Thermal gas rectification using a sawtooth channel
• Full Counting Statistics and Fluctuation Theorem for the Currents in the Discrete Model of Feynman's Ratchet
• Nanoswimmers in a ratchet potential: Effects of a transverse rocking force
• Dynamics of a Mechanical System with Multiple Degrees of Freedom out of Thermal Equilibrium
• Thermodynamic Emergence of a Brownian Motor