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Volume and entropy in abstract analytic number theory and thermodynamics

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Abstract

We develop the recent research [1] and introduce the notions of volume and entropy in abstract analytic number theory. The introduction of negative numbers in the generalized partition problem, together with the meaning of such a generalization in some applications of the theory, is discussed.

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References

  1. V. P. Maslov and V. E. Nazaikinskii, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds,” Math. Notes 100 (3–4), 421–428 (2016).

    Article  MathSciNet  Google Scholar 

  2. A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971; Amer. Math. Soc., Providence, RI, 1988).

    MATH  Google Scholar 

  3. J. Knopfmacher, Abstract Analytic Number Theory, in North-Holland Math. Library (North-Holland Publ., Amsterdam, 1975), Vol. 12.

  4. A. A. Karatsuba, Fundamentals of Analytic Number Theory (URSS, Moscow, 2004) [in Russian].

    Google Scholar 

  5. L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 5: Statistical Physics (Fizmatlit, Moscow, 2003) [in Russian].

    Google Scholar 

  6. V. P. Maslov and V. E. Nazaikinskii, “Bose–Einstein distribution as a problem of analytic number theory: the case of less than two degrees of freedom,” Math. Notes 100 (1–2), 245–255 (2016).

    Article  MathSciNet  Google Scholar 

  7. V. P. Maslov and V. E. Nazaikinskii, “Disinformation theory for bosonic computational media,” Math. Notes 99 (5–6), 895–900 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. P. Maslov, “Analytic number theory and disinformation,” Mat. Zametki 100 (4), 553–565 (2016) [Math. Notes 100 (3–4), 568–578 (2016)].

    Article  MathSciNet  Google Scholar 

  9. V. P. Maslov, “New Approach to Classical Thermodynamics,” Math. Notes 100 (1–2), 154–185 (2016).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. P. Maslov

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    V. P. Maslov, S. Yu. Dobrokhotov & V. E. Nazaikinskii

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia

    S. Yu. Dobrokhotov & V. E. Nazaikinskii

Authors
  1. V. P. Maslov
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  2. S. Yu. Dobrokhotov
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  3. V. E. Nazaikinskii
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Corresponding author

Correspondence to V. P. Maslov.

Additional information

Original Russian Text © V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 6, pp. 855–867.

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Maslov, V.P., Dobrokhotov, S.Y. & Nazaikinskii, V.E. Volume and entropy in abstract analytic number theory and thermodynamics. Math Notes 100, 828–834 (2016). https://doi.org/10.1134/S0001434616110225

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  • DOI: https://doi.org/10.1134/S0001434616110225

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