A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α−diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in t...

The Sharma-Mittal entropies generalize the celebrated Shannon, Rényi and Tsallis entropies. We report a closed-form formula for the Sharma-Mittal entropies and relative entropies for arbitrary exponential family distributions. We instantiate explicitly the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. PACS numbers: 03.65.Ta, 03.67.-a Submitted to...

Based on the data from the Chinese financial market, this paper focuses on analyzing three types of network entropies of the financial market, namely, Shannon, Renyi and Tsallis entropies. The findings suggest that Shannon entropy can reflect the volatility of the financial market, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi...

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and...

We discuss entropy definition for composite systems composed of two Tsallis (or Rényi) systems with different q indices using the bi-composability nature. The most general bi-composable entropy form is given.

We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscop...