Related papers: Nonextensive statistics based on Landsberg-Vedral …
Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the…
Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve…
A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis…
Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and…
This work puts into mathematical, statistical mechanical, and thermodynamical context the initial stages of the genesis of tornado-like vortices with the aim to be consistent with the current state of knowledge of the process of…
We study the thermodynamic properties of solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation. First we study the nonextensive grand canonical distribution function and the…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and…
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,…
Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal…
In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of…
We discuss the basic transport phenomena in gases and plasmas obeying the $q$-nonextensive velocity distribution (power-law). Analytical expressions for the thermal conductivity ($K_q$) and viscosity ($\eta_q$) are derived by solving the…
Recently we have demostrated that the nonextensitivity parameter q occuring in some applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is, in the q>1 case, given entirely by the fluctuations of…
We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made…
Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace…
The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive…
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…
It is pointed out that the Tsallis entropy functional represented in terms of the escort distribution is not concave of the entropic index $q$ is less than unity. It is emphasized that the escort distribution is a secondary object…