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Thermodynamic States and Their Stabilities

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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

A cursory survey of laws of thermodynamics relevant to the problems of phase transformations is given. Although similar information can be found in other textbooks, e.g., [1], the succinct presentation of the basic ideas and methods is helpful for understanding the general concepts in phase transformations.

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Notes

  1. 1.

    Characterizing a system by the number of particles does not mean assuming a microscopic approach.

  2. 2.

    Do not confuse them with the hidden variables in quantum mechanics.

  3. 3.

    Often this definition is applied to systems where X is composition of the state; however, nothing restricts us against expanding this definition on the states of general nature.

  4. 4.

    Except for the case when using the Galilean invariance, the stationary state can be reduced to the equilibrium one.

  5. 5.

    Relative to functions close to the extremal.

References

  1. E.A. Guggenheim, Thermodynamics. An Advanced Treatment for Chemists and Physicists (Elsevier, North Holland, Amsterdam, 1967)

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  2. S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (North Holland, Amsterdam, 1962)

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  3. P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, Inc., San Diego, CA, 1990)

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  4. P. Collet, J.-P. Eckmann, Instabilities and Fronts in Extended Systems (Princeton University Press, Princeton, NJ, 1990)

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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.

    Verify in Example 1.1 that all terms of the series (1E.3) comply with the boundary conditions of the problem.

  2. 2.

    Analyze stability of the nonlinear heat equation: \( \frac{dX}{dt}=\lambda {\nabla}^2X+\alpha X-{X}^{\mathsf{3}} \).

  3. 3.

    Give examples of other hidden variables in thermodynamics.

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Umantsev, A. (2023). Thermodynamic States and Their Stabilities. 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_1

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