Fokker-Planck and Langevin Equations

  • Wilhelm Brenig


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
$$\dot p\left( t \right) + \gamma p\left( t \right) = F\left( t \right)$$
and the condition
$$\overline {F\left( t \right)} = 0$$
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)
$$\dot \bar p\left( t \right) + \gamma \bar p\left( t \right) = 0.$$


Correlation Function Gaussian White Noise Langevin Equation Interaction Picture Friction Term 
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Additional Reading

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