In this paper a kind of partial subadditivity of the entropy is investigated in probability theory and in matrix theory. We show some new inequalities related to the subadditivity of the standard entropy and its one-parameter generalization in the discrete case. The matrix analogues of the inequalities are also studied. The standard entropy is related to the function −x log x, but here some oth...

We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis’ non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press (condmat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structur...

How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the complex of the complex networks. In this paper, a new method which is based on the Tsallis entropy is proposed to describe the complex of the complex networks. The results in this paper show that the complex of the complex networks not only decided by t...

A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between Tsallis entropy and the one-dimensional correlated anomalous diffusion equation is established. It is also developed explicitly a WKB-like method for second order ...

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...

In this paper a novel feature extraction method for image processing via PCNN and Tsallis entropy is presented. We describe the mathematical model of the PCNN and the basic concept of Tsallis entropy in order to find a recognition method for isolated objects. Experiments show that the novel feature is translation and scale independent, while rotation independence is a bit weak at diagonal angle...

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...

Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theo...

Landsberg’s notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome deficiencies of entropy as a measure of disorder due to extensivity. We generalize Landsberg’s concept to three classes of extended entropies: Rényi, Tsallis and Landsberg-Vedral. Three examples are treated, including one based on the logistic ...