Skip to main content
Log in

Generalized Ehrenfest's approach to phase transitions in multicomponent systems in the presence of an electromagnetic field

  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

The path of a transformation is defined and discussed in the framework of classical thermodynamics. The Ehrenfest's approach to the theory of higher order transition is generalized to heterogeneous systems of r components in the presence and in the absence of electromagnetic fields. By introducing a state label the phase transitions, in proximity of singular points, are analysed in terms of the stability theory. Systems, in the presence and in the absence of a magnetic field are discussed in some detail. It is shown that the Ehrenfest approximation about the transition of 2nd order is physically unstable.

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

  • P.W. Anderson, Basic Notions of Condensed Matter Physics (Perseus Publishing, 1997)

  • A.B. Pippard, Classical Thermodynamic (Cambridge University Press, Cambridge, 1957)

  • H. Callen, Thermodynamics and an Introduction to Thermostatics 2nd edn. (Wiley, New York, 1985)

  • G. Astarita, Thermodynamics: an advanced textbook for chemical engineers (Plenum Press, New York, 1989)

  • J.W. Gibbs, Collected Works (Longman Green & Co. Inc., New York, 1928)

  • J.W. Gibbs, Commentary on Collected Works (Yale University Press, New Haven, Conn., 1928)

  • Sommerfeld, Thermodynamics and statistical mechanics (Academic Press. Inc. Publisher, New York, 1950)

  • C. Charatheodory, Math. Ann. 67, 335 (1909)

    Google Scholar 

  • J.A. Schouten, W. van der Kulk, Pfaff's problem and its generalizations (Oxford University Press, New York, 1949)

  • P.T. Landsberg, Thermodynamics with Quantum Statistical Illustrations (Interscience, New York, 1961)

  • P. Ehrenfest, Leiden Comm. Suppl. 75b (1933)

  • G. Jaeger, Arch. Hist. Exact Sci. 53, 51 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • N. Goldenfeld, Lectures on Phase Transitions and Renormalization Group (Perseus Publishing, 1992)

  • V.L. Newhouse, Applied Superconductivity (John Wiley & Sons, Inc., New York, 1964)

  • D. Shoenberg, Superconductivity (Cambridge University Press, London, 1960)

  • R.N. Haward, The Physics of Glassy Polymers (Applied Science Publ., London, 1973)

  • P.G. de Gennes, J. Prost, The physics of Liquid Crystals (Clarendon Press, 1995)

  • Y. Zimmels, Phys. Rev. E 52, 1452 (1995)

    Article  ADS  Google Scholar 

  • E.M, Lifshitz, L.D. Landau, L.P. Pitaevskii, Electrodynamics of Continous Media, 2nd edn. (Butterworth-Heinemann, 1984)

  • I.A. Privorotskii, Rep. Prog. Phys. 35, 115 (1972)

    Article  ADS  Google Scholar 

  • J.G. Kirkwood, I. Oppenheim, Chemical Thermodynamics (McGraw-Hill, New York, 1961)

  • L. Mistura, J. Phys. A 12, 1527 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  • V.I. Smirnov, A Course in Higher Mathematics (Pergamon Press, Oxford, 1964)

  • E.A. Coddington, N. Levinson, Theory of ordinary differential equations (McGraw-Hill Press, 1955)

  • V.I. Arnold, Ordinary Differential Equations (M.I.T. Press, 1973)

  • R.L. Scott, Ber. Bunsenges, Phys. Chem. 76, 296 (1972)

    Google Scholar 

  • J.S. Rowlinson, F.L. Swinton, Liquids and Liquids mixtures, 2nd edn. (Butterworths, London, 1982)

  • S.B. Kiselev, J.C. Rainwater, Fluid Phase Equilib. 141, 129 (1977)

    Article  Google Scholar 

  • J. Jiang, J.M. Prausnitz, J. Chem. Phys. 111, 5964 (1999)

    Article  ADS  Google Scholar 

  • V.A. Agayan, M.A. Anisimov, J.V. Sengers, Phys. Rev. E 64, 6125 (2001)

    Article  ADS  Google Scholar 

  • J.M.H. Levelt Senger, R.F. Chang, G. Morrison., ACS Symp. Ser. 300, 110 (1986)

    Article  Google Scholar 

  • I. Prigogine, R. Defay, Chemical Thermodynamics (Longmans, New York, 1954)

  • M.W. Zemansky, Heat and Thermodynamics (McGraw-Hill, 1968)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Ambrosone.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ambrosone, L., Fontana, F. Generalized Ehrenfest's approach to phase transitions in multicomponent systems in the presence of an electromagnetic field. Eur. Phys. J. B 48, 537–545 (2005). https://doi.org/10.1140/epjb/e2006-00005-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2006-00005-5

Keywords

Navigation