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

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.