Related papers: Tsallis entropy induced metrics and CAT(k) spaces
The Tsallis and R\'enyi entropies are important quantities in the information theory, statistics and related fields because the Tsallis entropy is an one parameter generalization of the Shannon entropy and the R\'enyi entropy includes…
For an expansive homeomorphism, we investigate the relationship among dimension, entropy, and Lyapunov exponents. Motivated by Young's formula for surface diffeomorphisms, which links dimension and measure-theoretic entropy with hyperbolic…
We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young inequalities are also given. In addition, operator inequalities for normalized positive linear…
In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend…
Tsallis has proposed a generalisation of the standard entropy, which has since been applied to a variety of physical systems. In the canonical ensemble approach that is mostly used, average energy is given by an unnromalised, or normalised,…
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…
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…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the elastic cross section, which is the primary observable for high energy particle scattering, by employing a…
We show that the mutually exclusive nature of classical and quantum correlations distributed in multi-party quantum systems can be characterized in terms of $q$-expectation. Using Tsallis-$q$ entropy and $q$-expectation, we first provide…
We study the entanglement entropy between (possibly distinct) topological phases across an interface using an Abelian Chern-Simons description with topological boundary conditions (TBCs) at the interface. From a microscopic point of view,…
Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…
We show, in two different ways, that the Tsallis' partition function and its derivatives are related to thermodynamic quantities such as entropy, internal energy, etc., in the same way as in Boltzmann-Gibbs' formalism, with the Lagrange…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
The Lagrangian technique of Niven (2004, Physica A, 334(3-4): 444) is used to determine the constrained forms of the Tsallis entropy function - i.e. Lagrangian functions in which the probabilities of each state are independent - for each…
The exact analytical formulas for the transverse momentum distributions of the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles with nonzero mass in the framework of the Tsallis normalized and Tsallis unnormalized…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space…