Skip to main content
SpringerLink
Log in

Thermodynamic stability, critical points, and phase transitions in the theory of partial distribution functions

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the stability of the minimum of the thermodynamic potential treated as a functional of partial densities or correlation functions. We show that the loss of stability is related to critical points of thermodynamic functions. Curves or points of phase transitions of the first kind are determined by comparing the thermodynamic potentials of different phases, and the condition for loss of stability with respect to density fluctuations can be taken as the phase transition criterion only approximately. Phase transitions of the second kind are related to the loss of stability with respect to the pair correlation fluctuations.

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. K. Huang, Statistical Mechanics, Wiley, New York (1963).

    Google Scholar 

  2. B. T. Geilikman, The Statistical Theory of Phase Transitions [in Russian], Gos. Izdat. Tekhn.-Teor. Lit., Moscow (1954).

    Google Scholar 

  3. É. A. Arinshtein, Theor. Math. Phys., 124, 972–981 (2000); 143, 615–624 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  4. E. A. Arinshtein and R. M. Ganopol’skii, Theor. Math. Phys., 131, 681–689 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Vol. 1, Wiley-Interscience, New York (1975).

    MATH  Google Scholar 

  6. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics [in Russian], Vol. 5, Statistical Physics, Nauka, Moscow (1976); English transl. prev. ed., Pergamon Press Ltd., London (1958).

    Google Scholar 

  7. C. A. Crockston, Liquid State Physics, Cambridge Univ. Press, Cambridge (1974).

    Google Scholar 

  8. E. A. Arinshtein, Theor. Math. Phys., 148, 1147–1158 (2006).

    Article  MathSciNet  Google Scholar 

  9. É. A. Arinshtein, Theor. Math. Phys., 151, 571–585 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations [in Russian], Nauka, Moscow (1965); English transl.: (Transl. Math. Monogr., Vol. 22), Amer. Math. Soc., Providence, R. I. (1968).

    Google Scholar 

  11. É. A. Arinshtein, Theor. Math. Phys., 138, 107–117 (2004).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tyumen State University, Tyumen, Russia

    É. A. Arinshtein

Authors
  1. É. A. Arinshtein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to É. A. Arinshtein.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 512–523, June, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arinshtein, É.A. Thermodynamic stability, critical points, and phase transitions in the theory of partial distribution functions. Theor Math Phys 155, 949–958 (2008). https://doi.org/10.1007/s11232-008-0079-7

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-008-0079-7

Keywords

Search

Navigation