We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal distributions within O(q − 1) and in highand lowtemperature limits, q being the entropic index [H. Hasegawa, Phys. Rev. E 80 (2009) 011126]. Three types of G...

A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as for the discussion of a whole new class of measures. As a special case, a generalization of the measure proposed by Landsberg and his co-workers based on the...

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the s...

Multilevel thresholding is a method that is widely used in image segmentation. The thresholding problem is treated as an optimization problem with an objective function. In this article, a simple and histogram based approach is presented for multilevel thresholding in image segmentation. The proposed method combines Tsallis objective function and Particle Swarm Optimization (PSO). The PSO algor...

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Bolt...

We propose a nonextensive information-theoretic measure called Jensen-Tsallis divergence, which may be defined between any arbitrary number of probability distributions, and we analyze its main theoretical properties. Using the theory of majorization, we also derive its upper bounds performance. To gain further insight into the robustness and the application of the Jensen-Tsallis divergence mea...

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. ...