Related papers: Inhomogeneous distribution particles in self-gravi…
We analyzed formation of small-scale inhomogeneities of particle spatial distribution (particle clustering) in a turbulent flow. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution,…
In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features…
Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
We derive the global phase diagram of a self-gravitating $N$-body system enclosed in a finite three-dimensional spherical volume $V$ as a function of total energy and angular momentum, employing a microcanonical mean-field approach. At low…
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed centre of mass…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics may turn to be relevant to the derivation of the second law of thermodynamics. In particular, the spreading of the…
The gravitational potential and the gravitational rotation field generated by a thin-disk mass distribution with exponential density are considered in the case when the force between any two mass elements is not the usual Newtonian one, but…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
We obtain the Maxwell-J\"uttner distribution function at first order in the post-Newtonian approximation within the framework of general relativity. Taking into account the aforesaid distribution function, we compute the particle four-flow…
Self-similarity induced by critical gravitational collapse is used as a paradigm to probe the mass distribution of subsolar objects. At large mass (solar mass and above) there is widespread agreement as to both the form and parameter values…