Fokker-Planck Equation

  title={Fokker-Planck Equation},
  author={Hannes Risken},
As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function. As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [1.1] and Planck [1.2]: many review… 


In this paper, we present a direct perturbative method to solving certain Fokker–Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The

Microscopic dynamics of nonlinear Fokker-Planck equations.

An approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations using a nonextensive generalization of the Wiener process to model thermal noise in electric circuits is proposed.

Deriving fractional Fokker-Planck equations from a generalised master equation

A generalised master equation is constructed from a non-homogeneous random walk scheme. It is shown how fractional Fokker-Planck equations for the description of anomalous diffusion in external

A General Solution of the Fokker-Planck Equation

The Fokker-Planck equation is useful to describe stochastic processes. Depending on the force acting in the system, the solution of this equation becomes complicated and approximate or numerical

Exact solution of the Fokker-Planck equation for a broad class of diffusion coefficients.

  • K. S. Fa
  • Mathematics, Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
The asymptotic shape of the random-walk model and power-law decay obtained from other approaches can be reproduced from the solutions of the Langevin equation, by employing two simple functions for g (x,t) .

Fluctuation theorem and an extended Fokker-Planck equation

Fluctuation in entropy production in stochastic dynamics is considered based on a Langevin equation. Starting from the path integral expression for the distribution function of the entropy production

Maximum Path Information and Fokker--Planck Equation

We present a rigorous method to derive the nonlinear Fokker–Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang

Brownian Motion, Equations of Motion, and the Fokker-Planck Equations

The chapters which follow deal with nonequilibrium processes. First, in chapter 8, we treat the topic of the Langevin equations and the related Fokker-Planck equations. In the next chapter, the

A general nonlinear Fokker-Planck equation and its associated entropy

Abstract.A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex



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The Pawula theorem states that the generalized Fokker-Planck equation with finite derivatives greater than two leads to a contradiction to the positivity of the distribution function. Though negative

Generalized Onsager-Machlup function and classes of path integral solutions of the Fokker-Planck equation and the master equation

We determine the path integral solution of a stochastic process described by a generalized Langevin equation with coordinate-dependent fluctuating forces and white spectrum. Since such equations do

Manifolds of equivalent path integral solutions of the Fokker-Planck equation

Path integral solutions of the multi-dimensional Fokker-Planck equation with variable dependent diffusion coefficients are deduced in a simple and exact manner. We show that the Onsager-Machlup

Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general

Fluctuations and nonlinear irreversible processes. II

This paper forms the second part of a study which reexamines the relationship between fluctuations and nonlinear irreversible processes. The scope of the previous paper is generalized to include

Path integral formulation of general diffusion processes

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Two particle model for the diffusion of interacting particles in periodic potentials

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Operator orderings and functional formulations of quantum and stochastic dynamics

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The Radiation Theories of Tomonaga, Schwinger, and Feynman

A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a

Operator ordering schemes and covariant path integrals of quantum and stochastic processes in Curved space

A method is given for the derivation of covariant path integral solutions of quantum and stochastic processes in curved space.The correspondence between operator ordering schemes and ordinary