Related papers: Is Galaxy Distribution Non-extensive and Non-Gauss…
Large-scale astrophysical systems are non-extensive due to their long-range force of gravity. Here we show an approach toward the statistical mechanics of such self-gravitating systems (SGS). This is a generalization of the standard…
Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the…
The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…
Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of…
There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…
The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the…
The density of states of self-gravitational system diverges when the particles are spread to infinity. Other problem based an inhomogeneous distribution of particles,which motivate the gravitational interaction. In this sense the…
In the present study, we analyze the radial velocity distribution as a function of different stellar parameters such as stellar age, mass, rotational velocity and distance to the Sun for a sample of 6781 single low--mass field dwarf stars,…
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…
With particular attention to the recently postulated introduction of a non-extensive generalization of Boltzmann-Gibbs statistics, we study the long-term stellar dynamical evolution of self-gravitating systems on timescales much longer than…
We study the non-Gaussian tail of the probability distribution function of density in cosmological N-Body simulations for a variety of initial conditions. We compare the behaviour of the non-Gaussian tail in the real space with that in the…
We present a study of 9 galaxy groups with evidence for non-Gaussianity in their velocity distributions out to 4R200. This sample is taken from 57 groups selected from the 2PIGG catalog of galaxy groups. Statistical analysis indicates that…
In order to investigate whether galaxy structures are compatible with the predictions of the standard LCDM cosmology, we focus here on the analysis of several simple and basic statistical properties of the galaxy density field. Namely, we…
Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies or interstellar molecular clouds. We study the origin of these properties…
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,…
In the framework of nonextensive statistical mechanics, the equilibrium structures of astrophysical self-gravitating systems are stellar polytropes, parameterized by the polytropic index n. By careful comparison to the structures of…
A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann-Gibbs (BG) statistical mechanics. Some of…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
We consider the conditional galaxy density around each galaxy, and study its fluctuations in the newest samples of the Sloan Digital Sky Survey Data Release 7. Over a large range of scales, both the average conditional density and its…