Related papers: Open Problems within Nonextensive Statistical Mech…
The nonadditive entropy introduced by Tsallis in 1988 has been used in different fields and generalizes the Boltzmann entropy extending the possibilities of application of the statistical methods developed in the context of Mechanics. Here…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
The problem of temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a "quasi-reversible process", it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of…
The nonextensive one-dimensional version of a hydrodynamical model for multiparticle production processes is proposed and discussed. It is based on nonextensive statistics assumed in the form proposed by Tsallis and characterized by a…
It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from…
We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…
A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as…
The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here,…
In this paper we extend our recent results [Physica A340 (2004)110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Renyi with the q-deformed version of Khinchin axioms to obtain the…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
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 describe a simple and accurate framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the formalism of Tsallis' generalized non-extensive thermostatistics.…
An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks,…
We apply non-extensive methods to the statistical analysis of fully developed turbulent flows. Probability density functions of velocity differences at distance r obtained by extremizing the Tsallis entropies coincide well with what is…
Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further…
The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we…
Within Tsallis' nonextensive statistics, a model is elaborated to address self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are…