### Abstract

We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time-dependent perturbation. This transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis. We find that the expression obtained is useful for the calculation of fundamental quantities of the system, and that it provides a physical basis for the decomposition of the forces in the Langevin description into effective driving, dissipative and random forces in a large-scale description.

Original language | English |
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Pages (from-to) | 3799-3812 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 38 |

Issue number | 17 |

DOIs | |

Publication status | Published - 2005 Apr 29 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and General*,

*38*(17), 3799-3812. https://doi.org/10.1088/0305-4470/38/17/006