Related papers: A Shannon-Tsallis transformation

Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…

This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…

We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of…

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…

We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…

The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes' rule which uses information in the form of…

We generalize the completely monotone conjecture ([CG15]) from Shannon entropy to the Tsallis entropy up for orders up to at least four. To this end, we employ the algorithm ([J\"un16, JM06a]) which employs the technique of systematic…

The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under…

The paper characterizes the Shannon (1948) and Tsallis (1988) entropies in a standard framework of decision theory, mixture sets. Procedural mixture sets are introduced as a variant of mixture sets in which it is not necessarily true that a…

We identify the result of the continuous wavelet transform with the difference of solutions of two hyperbolic partial differential equations, for which wavelet's shift and scale are considered as independent variables on 2D plane. The…

Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…

We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…

By using a fonctionelle of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general method. The essential equivalence between the MaxEnt process of the most…

There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…

Ill-posed inverse problems of the form y = X p where y is J-dimensional vector of a data, p is m-dimensional probability vector which cannot be measured directly and matrix X of observable variables is a known J,m matrix, J < m, are…

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous…

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…