Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 8

Full text in Russian (pdf)

Russian page


DOI  https://doi.org/10.30898/1684-1719.2020.8.1

UDC 519.216.2; 519.216.22; 519.246.8; 533.722




A.   V. Blank, N. A. Suhareva, M. V. Tsyganov

M.V.Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory, 1-2, Moscow 119991, Russia

The paper is received on July 21, 2020


Abstract. An analysis technique is described within of the non-extensive Tsallis thermodynamics for experimentally recorded time scans, for displacement vectors, and for the drift velocity of the beam energy center. The variations of the Boltzmann-Gibbs entropy, the q-deformed Tsallis entropy and the available states number of the statistical ensemble of the recorded positions of the collimated wave beam energy center and its drift velocity are determined. To determine the type of attractors of the studied stochastic process, the spectra of Lyapunov exponents for the positional parameters of the wave beam are analyzed.

Key words: non-extensive thermodynamics, q-entropy Tsallis, escort distribution, energy distribution, Lyapunov exponents.


1. Kolesnichenko A.V., Chetverushkin B.N. Derivation of hydrodynamic and quasi-hydrodynamic equations for transport systems based on statistics of Tsallis. Preprints of the Keldysh Institute of Applied Mathematics. 2014. P.8–32.

2. Kolesnichenko A.V. To the construction of the thermo- dynamics of quantum nonextensive systems in the framework of the statistics of Tsallis. Preprints of the Keldysh Institute of Applied Mathematics. 2019. P.16–44.

3. Tsallis C. Introduction to nonextensive statistical mechanics: approaching a complex world. Springer-Verlag NewYork. 2009. 381 p. https://doi.org/10.1007/978-0-387-85359-8

4. Abe S. Stability of Tsallis entropy and instabilities of R ́enyi and normalized Tsallis entropies: A basis for q-exponential distributions. Physical Review E. 2002. Vol.66. No.4. P.046134.

5. Bashkirov A.G., Vityazev A.V. Information entropy and power-law distributions for chaotic systems. Physica A: Statistical Mechanics and its Applications. 2000. Vol.277. No.1-2. P.136–145.

6. Bashkirov A.G. Renyi entropy as a statistical entropy for com plex systems. Theoretical and Mathematical Physics. 2006. Vol.149. No.2. P.1559–1573.

7. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics. 1988. Vol.52. No.1-2. P.479–487.

8. Curado Evaldo M.F., Tsallis C. Generalized statistical mechanics: connection with thermodynamics. Journal of Physics a: mathematical and general. 1991. Vol.24. No.2. P.L69.

9. Mariz Ananias M. On the irreversible nature of the Tsallis and Renyi entropies. Physics Letters A. 1992. Vol. 165. No. 5-6. P.409–411.

10. Matsak I.S., Kapranov V.V., Tugaenko V.Yu. et al. Super narrow beam shaping system for remote power supply at long atmospheric paths. Laser Resonators, Microresonators, and Beam Control XIX. 2017. Vol.10090. P.100900U.

11. Babanin E.A., Suhareva N.A., Vokhnik O.M. et al. Positional characteristics of generalized decentered elliptical Gaussian beams propagating through extended atmospheric paths. 2017 Days on Diffraction (DD). 2017. P.24–30.

12. Umarov S., Tsallis C., Steinberg S. On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan journal of mathematics. 2008. Vol. 76. No.1. P.307–328.

13. Zaripov R.G. Changes in the entropy and the Tsallis difference information during spontaneous decay and self-organization of nonextensive systems. Russian Physics Journal. 2001. Vol.44. No.11. P.1159–1165.

14. Zaripov R.G. On thermodynamic equilibrium of nonextensive systems. Technical physics. 2006. Vol.51. No.11. P.1393–1397.

15. Kolesnichenko A.V. To the construction of the thermodynamics of non-additive media on the basis of the statistics of Tsallis–Mendes– Plastino. Preprints of the Keldysh Institute of Applied Mathematics. 2018. P.23–28.

16. Kolesnichenko A.V. Modification in the framework of nonadditive Tsallis statistics of the gravitational instability criterions of astrophysical disks. Matematicheskoe modelirovanie - Mathematical Simulation. 2016. Vol.28. No.3.
P. 96–118. (In Russian)

17. Cao L. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena. 1997. Vol.110. No.1-2. P.43–50.

18. Rainer K.H., Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1999. Vol.9. No.2. P.413–435.

19. Rosenstein M.T, Collins J.J, De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena. 1993. Vol.65. No.1-2. P.117–134.


For citation:

Blank A.V., Suhareva N.A., Tsyganov M.V. Q-parametric positional parameters of the collimated wave beam at the atmospheric path output. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 8. https://doi.org/10.30898/1684-1719.2020.8.1 (In Russian)