Skip to main content
SpringerLink
Log in

Unbounded probability theory and multistep relaxation processes

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We develop the ideology of unbounded probability theory in which the notion of elementary event is not used and present a new (more general) definition of independent events. The proposed construction is based on natural sequences 1, 2, ..., N and distributions of the type “partitio numerorum.” Essential use is made of the mathematical phenomenon of “Bose-Einstein condensate” type, a familiar notion in quantum statistical physics. The derived construction can be applied to thermodynamics and multistep relaxation processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. P. Maslov and T. V. Maslova, “Unbounded probability theory and its applications”, Teor. Veroyatnost. Primenen. 57(3), 471–498 (2012).

    MathSciNet  Google Scholar 

  2. L. I. Mandelshtam and M. A. Leontovich, “On the theory of absorbtion of sound in a liquid,” Zh. Éxper. Teoret. Fiz. 7(3), 438–449 (1937).

    Google Scholar 

  3. V. P. Maslov, “The role of macroinstrument and microinstrument and the observable quantities in the new conception thermodynamics,” Russian J. Math. Phys. 20(1), 68–101 (2013).

    Google Scholar 

  4. V. P. Maslov, “The mathematical theory of classical thermodynamics,” Math. Notes 93(1) 102–136 (2013).

    Article  Google Scholar 

  5. V. P. Maslov, Asymptotic Methods and Perturbation Theory (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  6. L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1964) [in Russian].

    Google Scholar 

  7. A. N. Shiryaev, Foundations of Stochastic Financial Mathematics (Fazis, Moscow, 1998), Vols. 1 and 2 [in Russian].

    Google Scholar 

  8. A. M. Vershik, “Statistical mechanics of combinatorial partitions, and their limit shapes,” Funktsional. Anal. i Prilozhen. 30(2), 19 (1996) [Functional Anal. Appl. 30 (2), 90 (1996)].

    Article  MathSciNet  Google Scholar 

  9. V. P. Maslov, Threshold Levels in Economics, arXiv:0903.4783v2 [q-fin. ST], 3 Apr 2009.

    Google Scholar 

  10. P. Erdős, “On some asymptotic formulas in the theory of partitions,” Bull. Amer. Math. Soc. 52, 185–188 (1946).

    Article  MathSciNet  Google Scholar 

  11. V. P. Maslov and P. P. Mosolov, Nonlinear Wave Equations Perturbed by Viscous Term, De Gruyter Expositions in Mathematics 31 (Walter de Gruyter, Berlin-New York, 2000).

    Book  Google Scholar 

  12. (Hayka, Mockba, 2006). V. P. Maslov, Quantum Economics (Nauka, Moscow, 2006) [in Russian].

    Google Scholar 

  13. V. P. Maslov, “Effect of a measuring instrument in the “Bose condensate” of a classical gas in a phase transition and in experiments with negative pressure,” Teoret. Mat. Fiz. 175(1), 93–132 (2013) [Theoret. and Math. Phys. 175 (1), 526–558 (2013)].

    Google Scholar 

  14. V. P. Maslov, Thermodynamics as a Multistep Relaxation Process and the Role of Observables in Different Scales of Quantities, arXiv:1303.5307v1 [physics.gen-ph], 21 Mar 2013.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    V. P. Maslov

Authors
  1. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Maslov.

Additional information

Original Russian Text © V. P. Maslov, 2013, published in Matematicheskie Zametki, 2013, Vol. 93, No. 3, pp. 420–431.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. Unbounded probability theory and multistep relaxation processes. Math Notes 93, 451–459 (2013). https://doi.org/10.1134/S0001434613030115

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434613030115

Keywords

Search

Navigation