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After introducing the fundamental properties of self-gravitating systems, we present an application of Tsallis' generalized entropy to the analysis of their thermodynamic nature. By extremizing the Tsallis entropy, we obtain an equation of…
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…
The most probable state of an infinite self-gravitating gas in the dynamical equilibrium is defined by `gravitational haziness', a parameter representing many-body effects and formally like the temperature in the case of thermal…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
We investigate the thermodynamic properties of stellar self-gravitating system arising from the Tsallis generalized entropy. In particular, physical interpretation of the thermodynamic instability, as has been revealed by previous…
Self-gravitating system are non-equilibrium a priory. A new approach is proposed, which employs a non-equilibrium statistical operator into account inhomogeneous distribution of particles and temperature. The method involves the saddle -…
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…
Gravity and thermal energy are universal phenomena which compete over the stabilization of astrophysical systems. The former induces an inward pressure driving collapse and the latter a stabilizing outward pressure generated by random…
We propose an approach to find out when a self-gravitating system is in a quasi-equilibrium state. This approach is based on a comparison between two quantities identifying behavior of the system: a measure of interactions intensity and the…
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…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two…
In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation,…
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a…
In this paper we propose a notion of stability, that we call $\epsilon -N$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical…
We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…
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…
The present effort addresses the question about the existence of a well-defined thermodynamic limit for the astrophysical systems with the following power law form: to tend the number of particles, N, the total energy, E, and the…
We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct stationary states with non-zero temperature by minimizing the corresponding free…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…