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We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
Low surface brightness galaxies are an excellent laboratory where stars and baryonic matter act as tracers of the gravitational potential of the dark matter halo. If dark matter is modeled as a perfect fluid, then spherically symmetric and…
Systems with long-range (LR) forces, for which the interaction potential decays with the interparticle distance with an exponent smaller than the dimensionality of the embedding space, remain an outstanding challenge to statistical physics.…
The evolution and the statistical properties of an infinite gravitating system represent an interesting and widely investigated subject of research. In cosmology, the standard approach is based on equations of hydrodynamics. In the present…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the Press-Schechter…
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions --- a context in which subtle…
The dark matter hypothesis, which is not called into question here, explains why typical rotation curves of spiral galaxies do not follow a Keplerian profile. It is however not sufficient in itself to explain why the whole matter…
Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof,…
In this work, we submit the explanation of spectra of the rotary curves of galaxies on the basis of a vector theory of gravitation without regard to the dark matter hypothesis. We study the approximation of rotary curves in case of existing…
We will construct a theory which can explain the dynamics toward the steady state self-gravitating systems (SGSs) where many particles interact via the gravitational force. Real examples of SGS in the universe are globular clusters and…
In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…
We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both nonlinear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with…
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,…
The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems:…
Dynamics of spiral galaxies derived from a given surface mass density has been derived earlier in a classic paper. We try to transform the singular elliptic function in the integral into a compact integral with regular elliptic function.…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…