Skip to main content
SpringerLink
Log in

The fluctuation-dissipation theorem for contracted descriptions of Markov processes

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. F. Fox and G. E. Uhlenbeck,Phys. Fluids 13:1893 (1970).

    Google Scholar 

  2. E. H. Hauge and A. Martin-Löf,J. Stat. Phys. 7:259 (1973).

    Google Scholar 

  3. D. Bedeaux and P. Mazur,Physica 76:247 (1974).

    Google Scholar 

  4. M. G. Velarde and E. H. Hauge,J. Stat. Phys. 10:103 (1974).

    Google Scholar 

  5. T. S. Chow and J. J. Hermans,Physica 65:156 (1973).

    Google Scholar 

  6. D. Bedeaux, A. M. Albano, and P. Mazur,Physica 88A:574 (1977).

    Google Scholar 

  7. M. Gitterman,Rev. Mod. Phys. 50:85 (1978).

    Google Scholar 

  8. S. De Groot and P. Mazur,Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962), Chapter VIII; see also H. B. G. Casimir,Rev. Mod. Phys. 17:343 (1945).

    Google Scholar 

  9. R. F. Fox,J. Stat. Phys. 16:259 (1977);J. Math. Phys. 18:2331 (1977).

    Google Scholar 

  10. D. Forster,Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, Reading, Mass., 1975), Chapter 6.

    Google Scholar 

  11. M. S. Gitterman and V. M. Kontorovich,Sov. Phys.—JETP 20:1433 (1965).

    Google Scholar 

  12. T. C. Lubensky and M. H. Rubin,Phys. Rev. B 12:3885 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of British Columbia, Vancouver, B.C., Canada

    D. H. Berman

Authors
  1. D. H. Berman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berman, D.H. The fluctuation-dissipation theorem for contracted descriptions of Markov processes. J Stat Phys 20, 57–81 (1979). https://doi.org/10.1007/BF01013746

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01013746

Key words

Search

Navigation