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Critical indices as a consequence of Wiener quantization of thermodynamics

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Abstract

We construct a family of perfect gases depending on the critical value of the compressibility factor Z for pure gases. We show that the critical indices of actual simple liquids, like many other thermodynamic effects, easily and naturally follow from the concept of Wiener quantization of modern thermodynamics.

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References

  1. V. P. Maslov, Theor. Math. Phys., 165, 1699–1720 (2010).

    Article  Google Scholar 

  2. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 5, Statistical Physics, Nauka, Moscow (1976); English transl. prev. ed., Pergamon, Oxford (1968).

    Google Scholar 

  3. E. M. Apfel’baum and V. S. Vorob’ev, Russ. J. Math. Phys., 18, 26–32 (2011).

    Article  MathSciNet  Google Scholar 

  4. V. P. Maslov, Theor. Math. Phys., 101, 1466–1472 (1994).

    Article  MATH  Google Scholar 

  5. V. P. Maslov, Quantization of Thermodynamics and Ultrasecond Quantization [in Russian], IKI, Moscow (2001).

    Google Scholar 

  6. V. P. Maslov, Russ. J. Math. Phys., 18, 440–464 (2011).

    Article  Google Scholar 

  7. B. van der Pol and H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge Univ. Press, Cambridge (1950).

    MATH  Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 3, Quantum Mechanics: Non-Relativistic Theory, Nauka, Moscow (1974); English transl., Pergamon, Oxford (1978).

    Google Scholar 

  9. V. P. Maslov, Russ. Math. Surveys, 38, 1–42 (1983).

    Article  ADS  MATH  Google Scholar 

  10. M. S. Green, “Introduction,” in: Proc. Conf. on Phenomena in the Neighborhood of Critical Points (NBS Misc. Publ., Vol. 273, M. S. Green and J. V. Sengers, eds.), Natl. Bur. Stand., Washington (1966), pp. ix-xi.

    Google Scholar 

  11. D. Yu. Ivanov, Vestnik Siberian State Univ. of Telecommunications and Inform. Sci., 3, 94–104 (2009).

    Google Scholar 

  12. V. P. Maslov, Russ. J. Math. Phys., 18, 440–464 (2011); arXiv:1111.6106v1 [physics.gen-ph] (2011).

    Article  Google Scholar 

  13. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975).

    MATH  Google Scholar 

  14. D. Yu. Ivanov, Critical Behavior of Non-Ideal Systems [in Russian], Fizmatlit, Moscow (2003); English transl., Wiley-VCH, Berlin (2008).

    Google Scholar 

  15. W. Wagner, N. Kurzeja, and B. Pieperbeck, Fluid Phase Equilibria, 79, 151–174 (1992).

    Article  Google Scholar 

  16. N. Kurzeja, T. Tielkes, and W. Wagner, Int. J. Thermophys., 20, 531–562 (1999).

    Article  Google Scholar 

  17. V. P. Maslov, Math. Notes, 90, 533–547 (2011).

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    V. P. Maslov

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  1. V. P. Maslov
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Correspondence to V. P. Maslov.

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Dedicated to the memory of dear Aleko

See the January and February issues of the journal, dedicated to A. N. Tavkhelidze.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 3, pp. 457–467, March, 2012.

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Maslov, V.P. Critical indices as a consequence of Wiener quantization of thermodynamics. Theor Math Phys 170, 384–393 (2012). https://doi.org/10.1007/s11232-012-0037-2

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  • DOI: https://doi.org/10.1007/s11232-012-0037-2

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