Skip to main content
Log in

Nonequilibrium fluctuations in μ space

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

Abstract

The properties of fluctuations inμ space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations inμ space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. H. Ernst and E. G. D. Cohen, inStudies in Statistical Mechanics, Vol. VIII, E. Montroll and J. L. Lebowitz, eds. (North-Holland Publishing Company, Amsterdam, 1981).

    Google Scholar 

  2. M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen,Physica (Utrecht) 45:127 (1969).

    Article  ADS  Google Scholar 

  3. Y. L. Klimontovich,Sov. Phys. JETP 6:753 (1958).

    ADS  Google Scholar 

  4. J. J. Hopfield and J. F. Bastin,Phys. Rev. 168:193 (1968).

    Article  ADS  Google Scholar 

  5. C. Cercignani,Trans. Theor. Stat. Phys. 2:211 (1972).

    Article  ADS  Google Scholar 

  6. H. van Beijeren, O. E. Lanford, III, J. L. Lebowitz, and H. Spohn,J. Stat. Phys. 22:237 (1980).

    Article  ADS  Google Scholar 

  7. V. V. Tolmachev,Sov. Phys. Dokl. 2:85 (1957).

    ADS  Google Scholar 

  8. G. H. Vinehard,Phys. Fluids 3:339 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  9. F. L. Hinton,Phys. Fluids 13:857 (1970).

    Article  ADS  Google Scholar 

  10. B. B. Saleeby and M. B. Lewis,Phys. Fluids 14:1931 (1971).

    Article  ADS  Google Scholar 

  11. R. Balescu,Equilibrium and Non-Equilibrium Statistical Mechanics (John Wiley & Sons, New York, 1975), Chap. 21.

    MATH  Google Scholar 

  12. S. Tsugé and K. Sagara,J. Phys. 12:403 (1975).

    Google Scholar 

  13. M. H. Ernst and J. R. Dorfman,Physica (Utrecht) 61:157 (1972).

    Article  ADS  Google Scholar 

  14. T. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman,Phys. Rev. Lett. 42:862 (1979).

    Article  ADS  Google Scholar 

  15. M. S. Green,Physica (Utrecht) 24:393 (1958).

    Article  ADS  Google Scholar 

  16. M. N. Barber, J. M. Blatt, and A. H. Opie,J. Stat. Phys. 13:379 (1975); J. M. Blatt and A. H. Opie,J. Stat. Phys. 13:385 (1975).

    Article  ADS  Google Scholar 

  17. Sh. M. Kogan,Theor. Math. Phys. (USSR) 10:94 (1972).

    Article  Google Scholar 

  18. T. Morita, H. Mori, and M. Tokuyama,J. Stat. Phys. 18:137 (1978).

    Article  ADS  Google Scholar 

  19. D. Ronis, I. Procaccia, and I. Oppenheim,Phys. Rev. A 19:1307 (1979).

    Article  ADS  Google Scholar 

  20. G. Ludwig,Physica (Utrecht) 28:841 (1962).

    Article  ADS  Google Scholar 

  21. A. Onuki,J. Stat. Phys. 18:475 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  22. I. Procaccia, D. Ronis, and I. Oppenheim,Phys. Rev. Lett. 42:287 (1979).

    Article  ADS  Google Scholar 

  23. T. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman,Phys. Rev. Lett. 44:472 (1980).

    Article  ADS  Google Scholar 

  24. A. M. S. Tremblay, E. D. Siggia, and M. R. Arai,Phys. Lett. 76A:57 (1980).

    Article  ADS  Google Scholar 

  25. M. H. Ernst, B. Cichocki, J. R. Dorfman, J. Sharma, and H. van Beijeren,J. Stat. Phys. 18:237 (1978).

    Article  ADS  Google Scholar 

  26. J. M. J. van Leeuwen and S. Yip,Phys. Rev. A1:1138 (1965).

    Article  Google Scholar 

  27. W. R. Chappell,J. Stat. Phys. 2:267 (1970).

    Article  ADS  Google Scholar 

  28. E. G. D. Cohen and T. H. Berlin,Physica (Utrecht) 26:717 (1960).

    Article  ADS  Google Scholar 

  29. O. Lanford, III,Soc. Math. Fr. Asterisq. 40:117 (1976).

    Google Scholar 

  30. H. Spohn, inProceedings of the Colloquium on “Random Fields” (Esztergom, Hungary, 1979).

    Google Scholar 

  31. S. V. Gantsevich, V. L. Gurevich, and R. Katilius,Sov. Phys. JETP 32:291 (1971).

    ADS  Google Scholar 

  32. M. Rostoker,Nucl. Fusion 1:1 (1960).

    Article  MathSciNet  Google Scholar 

  33. M. N. Rosenbluth and N. Rostoker,Phys. Fluids 5:776 (1962).

    Article  ADS  Google Scholar 

  34. D. Montgomery,Phys. Fluids 12:804 (1969); see also Ref. 9 for a correction.

    Article  ADS  Google Scholar 

  35. J. Dufty,Phys. Rev. A 13:2299 (1976).

    Article  ADS  Google Scholar 

  36. N. G. van Kampen, inTopics in Statistical Mechanics and Biophysics; A Memorial to Julius Jackson, R. A. Piccirelli, ed.,AIP-Conf. Proc. 27:153 (1976); (American Institute of Physics, New York, 1976).

    Chapter  Google Scholar 

  37. N. G. van Kampen,Phys. Lett. 50A:237 (1974).

    Article  ADS  Google Scholar 

  38. J. Logan and M. Kac,Phys. Rev. A 13:458 (1976).

    Article  ADS  Google Scholar 

  39. M. Kac and J. Logan, inStudies in Statistical Mechanics, Vol. VII, E. Montroll and J. L. Lebowitz, eds. (North-Holland Publishing Company, Amsterdam, 1979), p. 1.

    Google Scholar 

  40. O. Seeberg,J. Stat. Phys. 4:83 (1972).

    Article  ADS  Google Scholar 

  41. M. Malek-Mansour, L. Brenig, and W. Horsthemke,Physica (Utrecht) 88A:407 (1977).

    ADS  Google Scholar 

  42. C. van den Broeck and L. Brenig,Phys. Lett. 73A:298 (1979);Phys. Rev. A 21:1039 (1980).

    Article  ADS  Google Scholar 

  43. A. J. F. Siegert,Phys. Rev. 76:1708 (1949).

    Article  ADS  Google Scholar 

  44. R. Kubo, K. Matsuo, and K. Kitahara,J. Stat. Phys. 9:51 (1973).

    Article  ADS  Google Scholar 

  45. N. G. van Kampen,Physica (Utrecht) 96A:435 (1979).

    ADS  Google Scholar 

  46. Z. A. Akcasu,J. Seat. Phys. 16:33 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  47. R. F. Fox,Phys. Rep. 48:179 (1978).

    Article  ADS  Google Scholar 

  48. B. B. Kadomtsev,Sov. Phys. JETP 5:771 (1957).

    Google Scholar 

  49. M. Bixon and R. Zwanzig,Phys. Rev. 187:267 (1969).

    Article  ADS  MathSciNet  Google Scholar 

  50. R. F. Fox and G. E. Uhlenbeck,Phys. Fluids 13:1893, 2881 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  51. H. Mori,Prog. Theor. Phys. 33:423 (1965).

    Article  ADS  Google Scholar 

  52. H. Mori,Prog. Theor. Phys. 49:1516 (1973).

    Article  ADS  Google Scholar 

  53. J. Keizer,J. Chem. Phys. 63:398 (1975).

    Article  ADS  Google Scholar 

  54. M. Tokuyama and H. Mori,Prog. Theor. Phys. 56:1073 (1976).

    Article  ADS  Google Scholar 

  55. P. S. Lee and T. Y. Wu,Int. J. Theor. Phys. (GB) 7:267 (1973).

    Article  Google Scholar 

  56. H. Ueyama,Physica (Utrecht) 80A:98 (1979).

    ADS  MathSciNet  Google Scholar 

  57. M. Lax,Rev. Mod. Phys. 32:25 (1960).

    Article  ADS  Google Scholar 

  58. A. H. Kritz, G. V. Ramanathan, and G. Sandri, inKinetic Equations, R. L. Liboff and N. Rostoker, eds. (Gordon and Breach, New York, 1971), p. 307.

    Google Scholar 

  59. A. Z. Akcasu and J. J. Duderstadt,Phys. Rev. 188:479 (1969).

    Article  ADS  Google Scholar 

  60. A. Z. Akcasu and J. J. Duderstadt, inKinetic Equations, R. L. Liboff and N. Rostoker, eds. (Gordon and Breach, New York, 1971), p. 45.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ernst, M.H., Cohen, E.G.D. Nonequilibrium fluctuations in μ space. J Stat Phys 25, 153–180 (1981). https://doi.org/10.1007/BF01008484

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01008484

Key words

Navigation