Skip to main content
SpringerLink
Log in

Stationary solutions of the bogoliubov hierarchy equations in classical Statistical Mechanics, 1

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

This paper is the first part of the work whose subject is to investigate the set of stationary solutions ofB-B-G-K-Y hierarchy. We state that under some conditions on the interaction any stationary solution obeying certain restrictions of a general type corresponds to an equilibrium state (in the sense of Dobrushin-Lanford-Ruelle).

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. Lanford, O.E.: Commun. math. Phys.9, 169 (1968)

    Google Scholar 

  2. Lanford, O.E.: Commun. math. Phys.11, 257 (1969)

    Google Scholar 

  3. Sinai, Ja.G.: Theoret. i mathem. Phys. (in Russian)11, 248 (1972)

    Google Scholar 

  4. Sinai, Ja.G.: Vestnik MGU (in Russian), ser. mathem. i mech.1, 152 (1974)

    Google Scholar 

  5. Zemliakov, A.N.: Usp. mathem. nauk (in Russian)28: 1, 239 (1973)

    Google Scholar 

  6. Presutti, E., Pulvirenti, M., Tirozzi, B.: Preprint (1975)

  7. Marchioro, C., Pellegrinotti, A., Presutti, E.: Commun. math. Phys.40, 175 (1975)

    Google Scholar 

  8. Volkovyssky, K.L., Sinai, Ja.G.: Funkz. anal. i ego pril. (in Russian)5: 4, 19 (1971)

    Google Scholar 

  9. Sinai, Ja.G.: Funkz. anal. i ego pril. (in Russian)6: 1, 41 (1972)

    Google Scholar 

  10. de Pazzis, O.: Commun. math. Phys.22, 121 (1971)

    Google Scholar 

  11. Goldstein, S., Lebowitz, J.L.: Commun. math. Phys.37, 1 (1974)

    Google Scholar 

  12. Aizenman, M., Goldstein, S., Lebowitz, J.L.: Commun. math. Phys.39, 289 (1974)

    Google Scholar 

  13. Goldstein, S.: Commun. math. Phys.39, 303 (1974)

    Google Scholar 

  14. Lanford, O.E., Lebowitz, J.L.: Preprint (1975)

  15. Gurevich, B.M., Sinai, Ja.G., Suhov, Ju.M.: Usp. mathem. nauk (in Russian)28: 5, 45 (1973)

    Google Scholar 

  16. Bogoliubov, N.N.: Problems of the dynamical theory in Statistical Physics (in Russian). Moscow: Gostechizdat 1946

    Google Scholar 

  17. Gallavotti, G.: Nuovo Cimento57b, 208 (1968)

    Google Scholar 

  18. Gallavotti, G., Lanford, O.E., Lebowitz, J.L.: J. Math. Phys.11, 2898 (1970)

    Google Scholar 

  19. Petrina, D.Ja., Vidybida, O.K.: Preprint ITP 73-58E, Kiev, 1973

  20. Sinai, Ja.G., Suhov, Ju.M.: Theoret. i. mathem. Phys. (in Russian)19, 344 (1974)

    Google Scholar 

  21. Gurevich, B.M., Suhov, Ju.M.: Dokl. Acad. nauk SSSR (in Russian)223, (1975)

  22. Dobrushin, R.L.: Funkz. anal. i ego pril. (in Russian)2: 4, 31 (1968)

    Google Scholar 

  23. Dobrushin, R.L.: Funkz. anal. i ego pril. (in Russian)2: 4, 44 (1968)

    Google Scholar 

  24. Dobrushin, R.L.: Funkz. anal. i ego pril. (in Russian)3: 1, 27 (1969)

    Google Scholar 

  25. Lanford, O.E., Ruelle, D.: Commun. math. Phys.13, 194 (1968)

    Google Scholar 

  26. Kozlov, O.K.: Usp. mathem. nauk (in Russian)30: 5, 175 (1975)

    Google Scholar 

  27. Ruelle, D.: Phys. Rev. Letters27, 1040 (1970)

    Google Scholar 

  28. Lebowitz, J.L., Lieb, E.H.: Phys. Letters38A, 98 (1972)

    Google Scholar 

  29. Lenard, A.: Commun. math. Phys.30, 35 (1973)

    Google Scholar 

  30. Gallavotti, G., Verboven, E.: Nuovo Cimento28B, 274 (1975)

    Google Scholar 

  31. Van Hove, L.: Physica16, 137 (1950)

    Google Scholar 

  32. Gallavotti, G.: Miracle-Sole, S.: J. Math. Phys.11, 147 (1970)

    Google Scholar 

  33. Ruelle, D.: Ann. Phys.25, 109 (1963)

    Google Scholar 

  34. Schwartz, L.: Analyse mathematique,I. Paris: Hermann 1967

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Statistical Methods, Moscow State University, 117234, Moscow, USSR

    B. M. Gurevich

  2. Institute of Problems of Information Transmission, Academy of Sciences, 111024, Moscow, USSR

    Ju. M. Suhov

Authors
  1. B. M. Gurevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ju. M. Suhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. L. Lebowitz

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gurevich, B.M., Suhov, J.M. Stationary solutions of the bogoliubov hierarchy equations in classical Statistical Mechanics, 1. Commun.Math. Phys. 49, 63–96 (1976). https://doi.org/10.1007/BF01608637

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01608637

Keywords

Search

Navigation