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Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications

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  • Pavlos, G.P.
  • Karakatsanis, L.P.
  • Xenakis, M.N.
  • Pavlos, E.G.
  • Iliopoulos, A.C.
  • Sarafopoulos, D.V.

Abstract

We investigate Tsallis q-statistics for various complex physical systems. In particular, the Tsallis q-triplet is estimated for space plasmas, atmospheric dynamics, seismicity, and brain and cardiac activity. Remarkable agreement between theoretical Tsallis predictions and experimental estimations was observed in all cases. We also present theoretical extensions of Tsallis q-statistics for intermittent turbulence theory, non-equilibrium statistics, and fractal extension of dynamics.

Suggested Citation

  • Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Pavlos, E.G. & Iliopoulos, A.C. & Sarafopoulos, D.V., 2014. "Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 58-95.
    • Handle: RePEc:eee:phsmap:v:395:y:2014:i:c:p:58-95
    DOI: 10.1016/j.physa.2013.08.026
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    8. Pavlos, G.P. & Iliopoulos, A.C. & Tsoutsouras, V.G. & Sarafopoulos, D.V. & Sfiris, D.S. & Karakatsanis, L.P. & Pavlos, E.G., 2011. "First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2819-2839.
    9. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N., 2012. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6287-6319.
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    4. Antoniades, I.P. & Karakatsanis, L.P. & Pavlos, E.G., 2021. "Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    5. Karakatsanis, L.P. & Pavlos, G.P. & Iliopoulos, A.C. & Pavlos, E.G. & Clark, P.M. & Duke, J.L. & Monos, D.S., 2018. "Assessing information content and interactive relationships of subgenomic DNA sequences of the MHC using complexity theory approaches based on the non-extensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 77-93.
    6. Miśkiewicz, Janusz, 2016. "Improving quality of sample entropy estimation for continuous distribution probability functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 473-485.
    7. Iliopoulos, A.C. & Nikolaidis, N.S. & Aifantis, E.C., 2015. "Portevin–Le Chatelier effect and Tsallis nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 509-518.

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