9,921 research outputs found
Geometrical aspects in Equilibrium Thermodynamics
We discuss different aspects of the present status of the Statistical Physics
focusing the attention on the non-extensive systems, and in particular, on the
so called small systems. Multimicrocanonical Distribution and some of its
geometric aspects are presented. The same could be a very atractive way to
generalize the Thermodynamics. It is suggested that if the Multimicrocanonical
Distribution could be equivalent in the Thermodynamic Limit with some
generalized Canonical Distribution, then it is possible to estimate the
entropic index of the non-extensive thermodynamics of Tsallis without any
additional postulates.Comment: 6 pages, RevTeX. Revised Versio
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
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
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 , being 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
Remarks about the microcanonical description of astrophysical systems
We reconsider some general aspects about the mean field thermodynamical
description of the astrophysical systems based on the microcanonical ensemble.
Starting from these basis, we devote a special attention to the analysis of the
scaling laws of the thermodynamical variables and potentials in the
thermodynamic limit. Geometrical considerations motivate a way by means of
which could be carried out a well-defined generalized canonical-like
description for this kind of systems, even being nonextensive. This interesting
possibility allows us to extend the applicability of the Standard Thermodynamic
methods, even in the cases in which the system exhibits a negative specific
heat. As example of application, we reconsider the classical Antonov problem of
the isothermal spheres.Comment: RevTex4, 10 pages, 6 eps figures. Submitted Version to PR
Basis of a non Riemannian Geometry within the Equilibrium Thermodynamics
Microcanonical description is characterized by the presence of an internal
symmetry closely related with the dynamical origin of this ensemble: the
reparametrization invariance. Such symmetry possibilities the development of a
non Riemannian geometric formulation within the microcanonical description of
an isolated system, which leads to an unexpected generalization of the Gibbs
canonical ensemble and the classical fluctuation theory for the open systems
(where the inverse temperature and the total energy E behave as complementary
thermodynamical quantities), the improvement of Monte Carlo simulations based
on the canonical ensemble, as well as a reconsideration of any classification
scheme of the phase transitions based on the concavity of the microcanonical
entropy.Comment: Revtex style. 21 pages and 10 eps figure
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