Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect.

@article{Sarracino2013TimeAO,
  title={Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect.},
  author={Alessandro Sarracino},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 5},
  pages={
          052124
        }
}
  • A. Sarracino
  • Published 4 November 2013
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by… 
View on PubMed
arxiv.org
16 Citations
Background Citations
4

Figures from this paper

16 Citations

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient*

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a…

Coulomb Friction Driving Brownian Motors

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is…

Negative mobility of a Brownian particle: Strong damping regime

High-temperature ratchets driven by deterministic and stochastic fluctuations.

General explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations.

Generalized fluctuation–dissipation relations holding in non-equilibrium dynamics

  • L. Caprini
  • Physics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2021
We derive generalized fluctuation–dissipation relations (FDR) holding for a general stochastic dynamics that includes as subcases both equilibrium models for passive colloids and non-equilibrium…

On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems.

The general formalism of generalized fluctuation-dissipation relations is illustrated with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.

Tracer’s Diffusion: Swimming Through the Grains

In this chapter I consider the stochastic dynamics of an intruder in a granular fluid. Under the same assumptions used to derive the Boltzmann equation, a Master Equation for the intruder’s velocity…

Heat, temperature and Clausius inequality in a model for active Brownian particles

Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles, which consists of an overdamped particle subject to Gaussian coloured noise, and it is shown that a Clausius inequality holds.

Symmetry of deterministic ratchets.

It is shown that a pulsating ratchet with a multiplicative structure of its potential energy cannot move directionally if the energy is of the universal symmetry type in time; this restriction is removed in the inertial regime, but only if the coordinate dependence of the energy does not belong to either symmetric or antisymmetric functions.

Nonequilibrium dynamics of piecewise-smooth stochastic systems

Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems.…

References

SHOWING 1-10 OF 72 REFERENCES

Ratchet effect driven by Coulomb friction: the asymmetric Rayleigh piston.

It is illustrated in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath as well as an explicit analytical expression for the average velocity of the piston in the rare collision limit.

Kinetics of a frictional granular motor.

In the large friction limit, the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation is obtained, and in the limit of large rotor mass and small friction, a Fokker-Planck equation is derived.

Brownian motion with dry friction: Fokker–Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid–solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in…

Singular features in noise-induced transport with dry friction

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry…

Granular Brownian motion with dry friction

The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently…

Exact power spectra of Brownian motion with solid friction

We study a Langevin equation describing the Brownian motion of an object subjected to a viscous drag, an external constant force and a solid friction force of the Coulomb type. In a previous work…

Nonlinear dissipation effect in Brownian relaxation.

  • A. PlyukhinA. Froese
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
In an ensemble of noninteracting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially, from a small nonlinear correction to the dissipative force.

Brownian ratchet in a thermal bath driven by Coulomb friction.

A new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts is proposed, paving the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.

Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the…

A Gallavotti–Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics

We extend the work of Kurchan on the Gallavotti–Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes…
...