Dynamic Tsallis Entropy for Simple Model Systems

• Authors: N Khusnutdinov , R Yulmetyev , N Emelyanova
• Languages of publication: EN

Abstracts

EN

In this paper we consider the dynamic Tsallis entropy and employ it for four model systems: (i) the motion of Brownian oscillator, (ii) the motion of Brownian oscillator with noise, (iii) the fluctuation of particle density in hydrodynamics limit as well as in (iv) ideal gas. We show that the small value of parameter non-extensivity 0 < q < 1 acts as a non-linear magnifier for small values of the entropy. The frequency spectra become more sharp and it is possible to extract useful information in the case of noise. We show that the ideal gas remains non-Markovian for arbitrary values of q.

Keywords

EN

65.40.Gr

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2006
• Volume: 109
• Issue: 2
• Pages: 199-217

Dates

published

2006-02

received

2005-09-02

Contributors

author

N Khusnutdinov

• Department of Theoretical Physics, Kazan State Pedagogical University, Mezhlauk 1, 420021, Kazan, Russia

author

R Yulmetyev

• Department of Theoretical Physics, Kazan State Pedagogical University, Mezhlauk 1, 420021, Kazan, Russia

author

N Emelyanova

• Department of Theoretical Physics, Kazan State Pedagogical University, Mezhlauk 1, 420021, Kazan, Russia

References

• 1. C. Beck, F. Schlogl, Thermodynamics of Chaotic Systems, Cambridge University Press, Cambridge 1993
• 2. S.A. Kaufman, The Origins of Order - Self-Organization and Selection in Evolution, Oxford University Press, Oxford 1993
• 3. I. Goychuk, P. Hanggi, Phys. Rev. E, 61, 4272, 2000
• 4. Yu.L. Klimontovich, Phys. Scr., 58, 549, 1998
• 5. V. Latora, M. Baranger, A. Rapisarda, C. Tsallis, Phys. Lett. A, 273, 97, 2000
• 6. D.J. Scapino, M. Sears, R.A. Ferel, Phys. Rev. B, 6, 3409, 1972
• 7. C. Tsallis, Braz. J. Phys., 29, 1, 1999
• 8. R.M. Yulmetyev, M.Ya. Kleiner, Nonlinear Phenomena in Complex Systems, 1, 80, 1998
• 9. R.M. Yulmetyev, F.M. Gafarov, Physica A, 273, 416, 1999; R.M. Yulmetyev, F.M. Gafarov, Physica A, 274, 381, 1999
• 10. R.M. Yulmetyev, F.M. Gafarov, D.G. Yulmetyeva, N.A. Emeljanova, Physica A, 303, 427, 2002
• 11. A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge 1995
• 12. C. Tsallis, J. Stat. Phys., 52, 479, 1988
• 13. A. Aczél, Z. Daróczy, On Measures of Information and Their Characterizations, Academic Press, New York 1975
• 14. R.M. Yulmetyev, N.A. Emeljanova, F.M. Gafarov, Physica A, 341, 649, 2004
• 15. V.Yu. Shurygin, R.M. Yulmetyev, V.V. Vorobjev, Phys. Lett. A, 148, 199, 1990
• 16. V.Yu. Shurygin, R.M. Yulmetyev, Zh. Eksp. Teor. Fiz., 99, 144, 1991 [Sov. Phys.-JETP, 72, 80, 1991]
• 17. R.M. Yulmetyev, N.R. Khusnutdinov, J. Phys. A, 27, 5363, 1994
• 18. H. Mori, Prog. Theor. Phys., 33, 423, 1965; 34, 765, 1965
• 19. R. Zwanzig, Phys. Rev., 124, 1338, 1961
• 20. M. Reed, B. Simon, Methods of Modern Mathematical Physics, Academic, New York 1972
• 21. R. Zwanzig, Ann. Rev. Phys. Chem., 16, 67, 1965
• 22. P. Résibois, M. De Leener, Classical Kinetic Theory of Fluids, Wiley, New York 1977
• 23. N.B. Vargaftik, Handbook of Physical Properties of Liquids and Gases: Pure Substances and Mixtures, 2nd ed., Hemisphere Pub, Washington 1983
• 24. N.R. Khusnutdinov, R.M. Yulmetyev 1995, Teor. Matem. Fiz., 105, 292, 1995 [Theor. Math. Phys., 105, 1426, 1995]
• 25. S. Abe, Physica A, 269, 403, 1999

Identifiers

DOI

10.12693/APhysPolA.109.199