On the dynamical anomalies in numerical simulations of selfgravitating systems

According to self-similarity hypothesis, the thermodynamic limit could be defined from the scaling laws for the system self-similarity by using the microcanonical ensemble. This analysis for selfgravitating systems yields the following thermodynamic limit: send N to infinity, keeping constant E/N^{(7/3)} and LN^{(1/3)}, in which is ensured the extensivity of the Boltzmann entropy S_{B}=lnW(E,N). It is shown how the consideration of this thermodynamic limit allows us to explain the origin of dynamical anomalies in numerical simulations of selfgravitating systems.Comment: RevTex4, 4 pages, no figure

Microcanonical Thermostatistical Investigation of the Blackbody Radiation

In this work is presented the microcanonical analysis of the blackbody radiation. In our model the electromagnetic radiation is confined in an isolated container with volume V in which the radiation can not escape, conserving this way its total energy, E. Our goal is to precise the meaning of the Thermodynamic Limit for this system as well as the description of the nonextensive effects of the generalized Planck formula for the spectral density of energy. Our analysis shows the sterility of the intents of finding nonnextensive effects in normal conditions: the traditional description of the blackbody radiation is extraordinarily exact. The nonextensive effects only appear in the low temperature region, however, they are extremely difficult to detect.Comment: 7pages, RevTeX, 2 jpj figure

Generalizing the Extensive Postulates

We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the microcanonical ensemble, but this time, considering its equivalence with some generalized canonical ensemble in the thermodynamic limit by means of the scaling properties of the fundamental physical observables.Comment: 5 pages, RevTeX, no figures, Revised Versio

Some geometrical aspects of the Microcanonical Distribution

In the present work is presented some considerations for a possible generalization of the Microcanonical thermoestatics (M.Th) of D.H.E. Gross.The same reveals a geometric aspect that commonly it has been disregarded so far: the local reparametrization invariance . This new characteristic leads to the needing of generalizing the methods of M.Th to be consequent with this property.Comment: 4pages, RevTeX. Revised versio

Thermo-Statistical description of the Hamiltonian non extensive systems: The reparametrization invariance

In the present paper we continue our reconsideration about the foundations for a thermostatistical description of the called Hamiltonian nonextensive systems (see in cond-mat/0604290). After reviewing the selfsimilarity concept and the necessary conditions for the ensemble equivalence, we introduce the reparametrization invariance of the microcanonical description as an internal symmetry associated with the dynamical origin of this ensemble. Possibility of developing a geometrical formulation of the thermodynamic formalism based on this symmetry is discussed, with a consequent revision about the classification of phase-transitions based on the concavity of the Boltzmann entropy. The relevance of such conceptions are analyzed by considering the called Antonov isothermal model.Comment: RevTex with 10 pages and 2 eps figure

Remarks about the Phase Transitions within the Microcanonical description

According to the reparametrization invariance of the microcanonical ensemble, the only microcanonically relevant phase transitions are those involving an ergodicity breaking in the thermodynamic limit: the zero-order phase transitions and the continuous phase transitions. We suggest that the microcanonically relevant phase transitions are not associated directly with topological changes in the configurational space as the Topological Hypothesis claims, instead, they could be related with topological changes of certain subset A of the configurational space in which the system dynamics is effectively trapped in the thermodynamic limit N→∞.Comment: RevTeX, 4 pages, no figure. Revised versio

Where the Tsallis Statistic is valid?

In the present paper are analysed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Tsallis Statistic only could be applied for one special class of the bordering systems, those with non exponential growth of the accessible states density in the thermodynamic limit and zero-order divergency behavior for the fundamental macroscopic observables, systems located in the chaos threshold.Comment: 9 pages, RevTe

Astrophysical Systems: A model based on the Self-similarity Scaling Postulates

In the present work, it is developed a formalism to deal with the macroscopic study of the astrophysical systems, which is based on the consideration of the exponential self-similarity scaling laws that these systems exhibit during the realization of the thermodynamic limit. Due to their scaling laws, these systems are pseudoextensive, since although they are nonextensive in the usual sense, they can be studied by the Boltzmann-Gibbs Statistics if an appropriate representation of the integrals of motion of the macroscopic description is chosen. As example of application, it is analyzed the system of classical identical particles interacting via Newtonian interaction. A renormalization procedure is used in order to perform a well-defined macroscopic description of this system in quasi-stationary states, since it can not be in a real thermodynamic equilibrium. Our analysis showed that the astrophysical systems exhibit self-similarity under the following thermodynamic limit: $E\to \infty ,$ $L\to 0,$ $N\to \infty ,$ keeping $E/N^{{7/3}}=$const, $LN^{{1/3}}=$const, where $L$ is the characteristic linear dimension of the system. It is discussed the effect of these scaling laws in the dynamical properties of the system. In a general way, our solution exhibits the same features of the Antonov problem: the existence of the gravitational collapse at low energies as well as a region with a negative heat capacity.Comment: 17 pages, RevTeX, 13 ps figures, Version with a detailed analysis of the Microcanonical Mean Field approximatio

The microcanonical theory and pseudoextensive systems

In the present paper are considered the self-similarity scaling postulates in order to extend the Thermodynamics to the study of one special class of nonextensive systems: the pseudoextensive, those with exponential behavior for the asymptotical states density of the microcanonical ensemble. It is shown that this kind of systems could be described with the usual Boltzmann-Gibbs' Distribution with an appropriate selection of the representation of the movement integrals. It is shown that the pseudoextensive systems are the natural frame for the application of the microcanonical thermostatistics theory of D. H. E. Gross.Comment: 4 pages, RevTeX, no figures, Submited to PR

Remarks about the thermodynamic limit in selfgravitating systems

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 characteristic linear dimension of the system, L, to infinity, keeping constant E/N^{\Lambda_{E}} and L/N^{\Lambda_{L}}, being \Lambda_{E} and \Lambda_{L} certain scaling exponent constant. This study is carried out for a system constituted by a non-rotating fluid under the influence of its own Newtonian gravitational interaction. The analysis yields that a thermodynamic limit of the above form will only appear when the local pressure depends on the energy density of fluid as $p=\gamma\epsilon$, being $\gamma$ certain constant. Therefore, a thermodynamic limit with a power law form can be only satisfied by a reduced set of models, such as the selfgravitating gas of fermions and the Antonov isothermal model.Comment: RevTex 4, 4 pages. Comments about the de Vega and Sanchez discussion with V. Laliena about the applicability of the diluted limit in selfgravitating system