Universality of non-extensive Tsallis statistics and time series analysis: theory and applications. (English) Zbl 1395.82124
Summary: 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.
MSC:
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62B10 | Statistical aspects of information-theoretic topics |
| 60K40 | Other physical applications of random processes |
Keywords:
non-extensive Tsallis statistics; fractal dynamics; non-equilibrium dynamics; fractal acceleration; fractal dissipation; intermittent turbulenceReferences:
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