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Fokker-Planck and Langevin Equations

  • Wilhelm Brenig

Abstract

There are some interesting relations between the Fokker-Planck equation and the Langevin equation, which we want to discuss in this chapter. We remind the reader, see Chap. 14, that from Langevin’s equation
$$\dot p\left( t \right) + \gamma p\left( t \right) = F\left( t \right)$$
(38.1)
and the condition
$$\overline {F\left( t \right)} = 0$$
(38.2)
for the average value of the stochastic force in an arbitary nonequilibrium situation, one can easily read off an equation for the time evolution of the average momentum \(\bar p\)(t)
$$\dot \bar p\left( t \right) + \gamma \bar p\left( t \right) = 0.$$
(38.3)

Keywords

Correlation Function Gaussian White Noise Langevin Equation Interaction Picture Friction Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Additional Reading

  1. Onsager, L., Machlup, S.: Phys. Rev. 91, 1505, 1512 (1953)MathSciNetADSMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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