Related papers: Tsallis and R\'{e}nyi deformations linked via a ne…
Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal…
The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss simple physical applications of a system in the contact with finite heat bath or with temperature fluctuations. With help of the…
Consider a pair of random vectors $(\mathbf{X},\mathbf{Y}) $ and the conditional expectation operator $\mathbb{E}[\mathbf{X}|\mathbf{Y}=\mathbf{y}]$. This work studies analytic properties of the conditional expectation by characterizing…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy…
The necessary conditions (NC) that reconcile canonical probability distributions obtained from the q-maximum entropy principle, subjected to both i) the additive duality of generalized statistics and ii) normal averages expectations with…
Within the Tsallis thermodynamics' framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be…
An existing conjecture states that the Shannon mutual information contained in the ground state wavefunction of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the…
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the…
We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon's or Tsallis' entropies in the concomitant variational problem. It is shown that the two…
The correlated probabilistic model introduced and analytically discussed in Hanel et al (2009) is based on a self-dual transformation of the index $q$ which characterizes a current generalization of Boltzmann-Gibbs statistical mechanics,…
We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…
We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis…
We introduce the Langevin deformation for the R\'enyi entropy on the $L^2$-Wasserstein space over $\mathbb{R}^n$ or a Riemannian manifold, which interpolates between the porous medium equation and the Benamou-Brenier geodesic flow on the…
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…
We investigate a two-parameter entropy introduced by Schw\"{a}mmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert W-function which has been used…