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Thermodynamic Fluctuations

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Field Theoretic Method in Phase Transformations

Part of the book series: Lecture Notes in Physics ((LNP,volume 1016))

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Abstract

As we noticed in Chap. 11, TDGLE is not able to describe a phase transition itself, only the evolution of the system after the transition. Obviously, something very important for the complete description of the system is missing from that scheme. What is it?

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Notes

  1. 1.

    See Appendix G for a discussion of different ways to average a quantity.

  2. 2.

    This quantity, however, may be random but for completely different reasons.

  3. 3.

    See Appendix G regarding dξ/dt.

References

  1. L.D. Landau, E.M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1958) §146

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  2. A.Z. Patashinski, V.L. Pokrovski, Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1982, (in Russian)), p. 39

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  3. J.S. Langer, M. Bar-on, H.D. Miller, Phys. Rev. A 11, 1417 (1975)

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  4. J.D. Gunton, M. Droz, Introduction to the Theory of Metastable States (Springer-Verlag, Heidelberg, 1983), p. 95

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  5. A. Umantsev, Phys. Rev. E 93, 042806 (2016)

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  6. L.D. Landau, E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1960), p. 74

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  7. D.W. Jordan, P. Smith, Nonlinear Ordinary Differential Equations (Clarendon Press, Oxford, 1990)

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  8. L.S. Ornstein, F. Zernike, Proc. Acad. Sci. (Amsterdam), 17, 793 (1914)

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Author information

Authors and Affiliations

  1. Department of Chemistry, Physics, and Materials Science, Fayetteville State University, Fayetteville, NC, USA

    Alexander Umantsev

Authors
  1. Alexander Umantsev
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Exercises

Exercises

  1. 1.

    Find the correlation radius of fluctuations near the stable states of the Landau potential.

  2. 2.

    Substitute (12.53) into (12.52) and verify that two types of averages appear in the final expression.

  3. 3.

    Verify that (12.91) is a solution of (12.90).

  4. 4.

    Verify that expression (12.93b) follows from expression (12.93a).

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Umantsev, A. (2023). Thermodynamic Fluctuations. In: Field Theoretic Method in Phase Transformations. Lecture Notes in Physics, vol 1016. Springer, Cham. https://doi.org/10.1007/978-3-031-29605-5_12

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