13 research outputs found
Fluctuation of energy in the generalized thermostatistics
We calculate the fluctuation of the energy of a system in Tsallis statistics
following the finite heat bath canonical ensemble approach. We obtain this
fluctuation as the second derivative of the logarithm of the partition function
plus an additional term. We also find an explicit expression for the relative
fluctuation as related to the number of degrees of freedom of the bath and the
composite system.Comment: 9 pages. submited to Physica
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
We uncover the dynamics at the chaos threshold of the logistic
map and find it consists of trajectories made of intertwined power laws that
reproduce the entire period-doubling cascade that occurs for . We corroborate this structure analytically via the Feigenbaum
renormalization group (RG) transformation and find that the sensitivity to
initial conditions has precisely the form of a -exponential, of which we
determine the -index and the -generalized Lyapunov coefficient . Our results are an unequivocal validation of the applicability of the
non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to
critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation
improvements. To appear published as a Rapid communication of PR
Two-dimensional maps at the edge of chaos: Numerical results for the Henon map
The mixing properties (or sensitivity to initial conditions) of
two-dimensional Henon map have been explored numerically at the edge of chaos.
Three independent methods, which have been developed and used so far for the
one-dimensional maps, have been used to accomplish this task. These methods are
(i)measure of the divergence of initially nearby orbits, (ii)analysis of the
multifractal spectrum and (iii)computation of nonextensive entropy increase
rates. The obtained results strongly agree with those of the one-dimensional
cases and constitute the first verification of this scenario in two-dimensional
maps. This obviously makes the idea of weak chaos even more robust.Comment: 4 pages, 3 figure
An Improved Description of the Dielectric Breakdown in Oxides Based on a Generalized Weibull distribution
In this work, we address modal parameter fluctuations in statistical
distributions describing charge-to-breakdown and/or
time-to-breakdown during the dielectric breakdown regime of
ultra-thin oxides, which are of high interest for the advancement of electronic
technology. We reobtain a generalized Weibull distribution (-Weibull), which
properly describes data when oxide thickness fluctuations are
present, in order to improve reliability assessment of ultra-thin oxides by
time-to-breakdown extrapolation and area scaling. The incorporation
of fluctuations allows a physical interpretation of the -Weibull
distribution in connection with the Tsallis statistics. In support to our
results, we analyze data of SiO-based MOS devices obtained
experimentally and theoretically through a percolation model, demonstrating an
advantageous description of the dielectric breakdown by the -Weibull
distribution.Comment: 5 pages, 3 figure
Nonextensive Entropies derived from Form Invariance of Pseudoadditivity
The form invariance of pseudoadditivity is shown to determine the structure
of nonextensive entropies. Nonextensive entropy is defined as the appropriate
expectation value of nonextensive information content, similar to the
definition of Shannon entropy. Information content in a nonextensive system is
obtained uniquely from generalized axioms by replacing the usual additivity
with pseudoadditivity. The satisfaction of the form invariance of the
pseudoadditivity of nonextensive entropy and its information content is found
to require the normalization of nonextensive entropies. The proposed principle
requires the same normalization as that derived in [A.K. Rajagopal and S. Abe,
Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis
for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review
Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
For a family of logistic-like maps, we investigate the rate of convergence to
the critical attractor when an ensemble of initial conditions is uniformly
spread over the entire phase space. We found that the phase space volume
occupied by the ensemble W(t) depicts a power-law decay with log-periodic
oscillations reflecting the multifractal character of the critical attractor.
We explore the parametric dependence of the power-law exponent and the
amplitude of the log-periodic oscillations with the attractor's fractal
dimension governed by the inflexion of the map near its extremal point.
Further, we investigate the temporal evolution of W(t) for the circle map whose
critical attractor is dense. In this case, we found W(t) to exhibit a rich
pattern with a slow logarithmic decay of the lower bounds. These results are
discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig
Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg
It was recently published by M. Nauenberg [1] a quite long list of objections
about the physical validity for thermal statistics of the theory sometimes
referred to in the literature as {\it nonextensive statistical mechanics}. This
generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the
following expression for the entropy:
S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv
-k\sum_{i=1}^W p_i \ln p_i) .
The author of [1] already presented orally the essence of his arguments in
1993 during a scientific meeting in Buenos Aires. I am replying now
simultaneously to the just cited paper, as well as to the 1993 objections
(essentially, the violation of "fundamental thermodynamic concepts", as stated
in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys.
Rev. E 67, 036114 (2003
Metastability, negative specific heat and weak mixing in classical long-range many-rotator system
We perform a molecular dynamical study of the isolated classical
Hamiltonian , known to
exhibit a second order phase transition, being disordered for and ordered otherwise ( total energy
and ). We focus
on the nonextensive case and observe that, for , a
basin of attraction exists for the initial conditions for which the system
quickly relaxes onto a longstanding metastable state (whose duration presumably
diverges with like ) which eventually crosses over to the
microcanonical Boltzmann-Gibbs stable state. The temperature associated with
the (scaled) average kinetic energy per particle is lower in the metastable
state than in the stable one. It is exhibited for the first time that the
appropriately scaled maximal Lyapunov exponent
, where, for all values of ,
numerically coincides with {\it one third} of its value for , hence
decreases from 1/9 to zero when increases from zero to unity,
remaining zero thereafter. This new and simple {\it connection between
anomalies above and below the critical point} reinforces the nonextensive
universality scenario.Comment: 9 pages and 4 PS figure
Uma proposta de levantamento de dados para a assistĂȘncia Ă famĂlia e ao cuidador de lesados medulares
Anisotropic Heisenberg surface on semi-infinite Ising ferromagnet : renormalization group treatment
We use a Migdal-Kadanoff-like renormalization group approach to study the critical behaviour of a semi-infinite simple cubic Ising ferromagnet whose (1, 0, 0) free surface contains anisotropic (in spin space) Heisenberg ferromagnetic interactions. The phase diagram presents three phases (namely the paramagnetic, the bulk ferromagnetic and the surface ferromagnetic ones) which join on a multicritical point The location of this point is calculated as a function of the anisotropy. The various universality classes of the problem are exhibited.Nous utilisons une transformation de renormalisation de Migdal-Kadanoff pour étudier le comportement critique d'un ferromagnétique d'Ising, cubique simple, cubique infini dont la surface libre (1, 0, 0) contient des interactions anisotropes (dans l'espace des spins) ferromagnétiques de Heisenberg. Le diagramme de phase présente trois phases (paramagnétique, ferromagnétique en volume et ferromagnétique en surface) qui se rejoignent en un point multicritique. Les coordonnées de ce point sont calculées en fonction de l'anisotropie. Les diverses classes d'universalité du problÚme sont mises en évidence