Related papers: Tsallis entropy and hyperbolicity
Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic…
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…
The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems…
We demonstrate and discuss the process of gaining information and show an example in which some specific way of gaining information about an object results in the Tsallis form of entropy rather than in the Shannon one.
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…
The aim of the present paper is to present a careful and accessible discussion of the formal aspects of Boltzmann-Gibbs and Tsallis entropies. We begin with a brief overview of Boltzmann-Gibbs entropy, highlighting its main properties and…
We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.
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…
Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this brief report we show that the generalized canonical…
The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…
In this letter, we study the limit behavior of the evolution of Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or…
It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…