Related papers: Spherical galaxy models as equilibrium configurati…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible…
We explore the mass distribution of material associated with galaxies from the observation of gravitational weak lensing for the galaxy mass correlation function with the aid of $N$-body simulations of dark matter. The latter is employed to…
Certain types of active systems can be treated as an equilibrium system with excess non-conservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles interacting with each other with both…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
We use the Millennium Simulation, a 10 billion particle simulation of the growth of cosmic structure, to construct a new model of galaxy clustering. We adopt a methodology that falls midway between the traditional semi-analytic approach and…
The critique against using Boltzmann's microcanonical entropy, an "ensemble measure", as foundation of statistics is rebuffed. The confusion of the microcanonical distribution with the exponential Boltzmann-Gibbs (``BG'') distribution is…
Violent relaxation during the collapse of a galaxy halo is known to be incomplete in realistic cases such as cosmological infall or mergers. We adopt a physical picture of strong but short lived interactions between potential fluctuations…
Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability…
The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
High-energy phenomena presenting strong dynamical correlations, long-range interactions and microscopic memory effects are well described by nonextensive versions of the canonical Boltzmann-Gibbs statistical mechanics. After a brief…
The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the…
In this paper, we study the distribution functions that arise naturally during self-similar radial infall of collisionless matter. Such matter may be thought of either as stars or as dark matter particles. If a rigorous steady state is…
The measured rotation velocity profiles of mature spiral galaxies are successfully described with a gravitational model consisting of a thin axisymmetric disk of finte radius. The disk is assumed uniformly thin but with variable radial mass…
We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the…
This paper describes a general investigation of stationary oscillations of galaxies. It begins with a linear analysis of modes of oscillation with continuous spectra of real frequencies. Such modes are gravitational analogues of the van…
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,…
The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). A broad spectrum of halos and halo groups are necessary to form from…