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. ...

Flow-rate measurement in rivers under different conditions is required for river management purposes including water resources planning, pollution prevention, and flood control. This study proposed a new discharge estimation method by using a mean velocity derived from a 2D velocity distribution formula based on Tsallis entropy concept. This procedure is done based on several factors which refl...

We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics. PACS number(s): 05.20.-y, 05.30.-d, 05.40.+j, 05.60.+w The generalized non-extensive statistics and the fractional exclusion statistics have excited great interest because o...

We prove a variety of improved uniform continuity bounds for entropies both classical random variables on an infinite state space and quantum states infinite-dimensional systems. obtain the first tight estimate Shannon entropy with countably alphabet. The proof relies new mean-constrained Fano-type inequality. then employ this result to derive energy-constrained bound von Neumann entropy. To de...

In this paper, we propose a new discriminative model named nonextensive information theoretical machine (NITM) based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random variables. Tsallis divergence is used to regularize the distribution of weight parameters and maximum unnormalized Tsallis entropy distribution is used to evaluate fitti...

In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of q-Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically equivalent to a rate-large-deviation-like functional. The result explains why the Wasserstein metric as well as the combination of it with the Tsallis-entropy play an ...

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...