Related papers: Galaxy Distributions and Tsallis Statistical Mecha…
Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive…
This pedagogical review addresses several issues related to statistical description of gravitating systems in both static and expanding backgrounds, focusing on the latter. After briefly reviewing the results for the static background, I…
We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press…
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for…
Gravitational Lensing is a UNIQUE tool to constrain the mass distribution of collapsed structures, this is particularly true for galaxies, either on a case by case basis using multiple images of background sources (such as quasars), or…
We show that starting with either the non-extensive Tsallis entropy in Wang's formalism or the extensive Renyi entropy, it is possible to construct the equilibrium statistical mechanics with non-Gibbs canonical distribution functions. The…
Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10^{-4} pc till 100 pc. Secondly, the galaxy distribution has been observed to be fractal in…
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…
The microcanonical partition function for self-gravitational system in three dimensional case has been found. Used approach from the field theory of statistical description of the system was tailored to gravitational interacting particles…
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…
It has been shown in the literature that effective gravitational constants, which are derived from Verlinde's formalism, can be used to introduce the Tsallis and Kaniadakis statistics. This method provides a simple alternative to the usual…
In Statistical Mechanics, Tsallis distributions were apparently conceived in connection with systems presenting long--range interactions. In fact, they were observed in numerical computations for models of such a type, as occurring in the…
We determine the galaxy counts-in-cells distribution from the Sloan Digital Sky Survey (SDSS) for 3D spherical cells in redshift space as well as for 2D projected cells. We find that cosmic variance in the SDSS causes the counts-in-cells…
A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…
We study the non-extensive Tsallis statistics and its applications to QCD and high energy physics, and analyze the possible connections of this statistics with a fractal structure of hadrons. Then, we describe how scaling properties of…
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…
We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that i) the coupling between the systems is weak, ii) the structure…
We present source code for the computer algebra system Mathematica that analyzes the distribution of nearby Galaxies using SDSS data. Download instructions are given, thus within 10 minutes, the reader can verify that galaxies are…
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…
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…