Abstract The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is considered and a property of factorization investigated. The property reflects a separation between the system being observed and the observer. App...

Space plasmas are frequently described by kappa distributions. Non-extensive statistical mechanics involves the maximization of the Tsallis entropic form under the constraints of canonical ensemble, considering also a dyadic formalism between the ordinary and escort probability distributions. This paper addresses the statistical origin of kappa distributions, and shows that they can be connecte...

This paper provides a “non-extensive” information theoretic perspective on the relationship between risk and incomplete states uncertainty. Theoretically and empirically, we demonstrate that a substitution effect between the latter two may take place. Theoretically, the “non-extensive” volatility measure is concave with respect to the standard (based on normal distribution) volatility measure. ...

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young’s inequality. We also give a generalized Han’s inequality.

The purpose of this short paper dedicated to the 60th anniversary of Prof.Constantin Tsallis is to show how the use of mathematical tools and physical concepts introduced by Burr, L˙ evy and Tsallis open a new line of analysis of the old problem of non-Debye decay and universality of relaxation. We also show how a finite characteristic time scale can be expressed in terms of a q-expectation usi...