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Journal of Statistical Physics

, Volume 20, Issue 1, pp 57–81 | Cite as

The fluctuation-dissipation theorem for contracted descriptions of Markov processes

  • D. H. Berman
Articles

Abstract

It is shown that if the Onsager-Casimir relations and the fluctuationdissipation theorem are valid for a stationary, Gaussian, Markov process in anN-dimensional space, then these relations are valid when the process is projected into a subspace of the original space. Both time-reversal-even and time-reversal-odd variables are allowed. Previous derivations of the fluctuation-dissipation theorem for Brownian motion from fluctuating hydrodynamics are special cases of the present result. For the Brownian motion problem, the fluctuation-dissipation theorem is proven for the case of a compressible, thermally conducting fluid with a nonlocal equation of state. Arbitrary slip boundary conditions are considered as well.

Key words

Fluctuation-dissipation theorem Onsager-Casimir relations contracted description Brownian motion 

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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • D. H. Berman
    • 1
  1. 1.Department of ChemistryUniversity of British ColumbiaVancouverCanada

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