A nonextensive thermodynamical equilibrium approach in e+e−→hadronse^+ e^- \to hadrons

We show that the inclusion of long distance effect, expected in strong interactions, through a nonextensive thermodynamical approach is able to explain the experimental distribution of the transverse momentum of the hadrons with respect to the jet axis ($p_{t}$) $e^+ e^- \to hadron$ reaction. The observed deviation from the exponential behavior, predicted by the Boltzmann-Gibbs thermodynamical treatment, is automatically recovered by the nonextensive Tsallis statistics used here. We fitted the observed $p_{t}$ spectrum in the range of 14 GeV to 161 GeV and obtained, besides a good fit, the theoretical important fact that the temperature becomes independent of the primary energy.Comment: 9 pages, 2 eps figure

Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and focus on the unique value $q_{sen}<1$ for which the entropic form $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.Comment: Final version with new Title and small modifications. REVTeX, 8 pages and 4 eps figure

Generalized Heisenberg Algebras and Fibonacci Series

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.Comment: 24 pages, 2 figures, subfigure.st

Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$, $\theta$ and $\nu$ are real parameters. This equation unifies the anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). Exact point-source solution is obtained, enabling us to describe a large class of subdiffusion ($\theta > (1-\nu)d$), normal diffusion ($\theta= (1-\nu)d$) and superdiffusion ($\theta < (1-\nu)d$). Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.Comment: 3 pages, 2 eps figure

Logarithmic diffusion and porous media equations: a unified description

In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.Comment: 5 pages. To appear in Phys. Rev.

Gravitational Wave Emission from a Bounded Source: the Nonlinear Regime

We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Amongst the obtained results of the nonlinear evolution, one of the most impressive is the fact that the distribution of the mass fraction extracted by gravitational wave emission satisfies the distribution law of nonextensive statistics and this result is independent of the initial configurations considered.Comment: 3 page, 1 figure, proceedings of the X Marcel Grossmann Meeting 22-26 July, 2003, Rio de Janeir

Generating functions for generalized binomial distributions

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available.Comment: PDFLaTex, 27 pages, 5 figure

Phase diagram of a 2D Ising model within a nonextensive approach

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for $q\neq 1$. A $q -$ phase diagram (critical temperature vs. the entropic parameter $q$) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index $q$. It is shown that such phases favors some energy levels of magnetization states. It is also showed that the contribution of the Tsallis cutoff is essential to the existence of phase transitions

Nonextensivity of the cyclic Lattice Lotka Volterra model

We numerically show that the Lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a {\it finite} production, per unit time, of the nonextensive entropy $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i \ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode (growing droplet), and for $q=0$ for the $d=1$ one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is for the first time exhibited for a many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure

Fusió de la teoria del decreixement i la de bens comuns

L'objectiu d'aquest article científic és començar a treballar en la fusió de dues línies de pensament les quals, ja per si soles, tenen una gran potència explicativa: La teoria del decreixement i la de bens comuns. Parlem de fusió ja que, més que posar en relació aquestes dues línies de pensament, es té la intenció d'aportar evidències de que el decreixement ha d'ésser comunal, i que la conservació i producció respectuosa dels bens comuns només es pot donar plenament en el marc del decreixement. En l'ànima d'aquest assaig batega un intent de reformular l'esquerra. Es busca trobar institucions socials en les que s'uneixin la solidaritat social i l'empoderament polític, per a assolir una comunitat en la qual el creixement estigui sotmès al ritme de regeneració de la biosfer