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

Metastability, negative specific heat and weak mixing in classical long-range many-rotator system

We perform a molecular dynamical study of the isolated $d=1$ classical Hamiltonian ${\cal H} = {1/2} \sum_{i=1}^N L_i^2 + \sum_{i \ne j} \frac{1-cos(\theta_i-\theta_j)}{r_{ij}^\alpha} ;(\alpha \ge 0)$, known to exhibit a second order phase transition, being disordered for $u \equiv U/N{\tilde N} \ge u_c(\alpha,d)$ and ordered otherwise ($U\equiv$ total energy and ${\tilde N} \equiv \frac{N^{1-\alpha/d}-\alpha/d}{1-\alpha/d}$). We focus on the nonextensive case $\alpha/d \le 1$ and observe that, for $u<u_c$, 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 $N$ like ${\tilde N}$) 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 $\lambda_{u<u_c}^{max}(metastable) \propto N^{-\kappa_{metastable}} ;(N \to \infty)$, where, for all values of $\alpha/d$, $\kappa_{metastable}$ numerically coincides with {\it one third} of its value for $u>u_c$, hence decreases from 1/9 to zero when $\alpha/d$ 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

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

PACS. 05.20.-y Statistical mechanics - 05.45.+b Theory and models of chaotic systems - 05.70.Ln Nonequilibrium thermodynamics, irreversible processes,

The use of in-situ ion-irradiation/TEM techniques to study radiation damage in SiC

SiC is a material currently under consideration to be used in future generations of fission and fusion reactors where it will be subjected to high temperatures and significant fluxes of energetic neutrons. The work reported in this thesis aims to answer some outstanding issues of the behaviour of SiC at high temperature during irradiation by high-energy neutrons in combination with a build-up of helium (from both transmutation reactions and by direct implantation). These processes have been simulated by in-situ ion-irradiation / TEM at the MIAMI and JANNuS facilities. This thesis contains the results of experiments which investigated the nucleation and growth of helium bubbles in SiC and the behaviour of these helium bubbles under high energy heavy ion-irradiation. Our conclusions are that helium bubbles in SiC are extremely stable at high temperatures and during high-energy ion-irradiation. However, we have discovered that there is a significant effect on the bubbles attributable to either electron beam irradiation alone or the synergistic effect of the electron beam and ionirradiation which causes helium bubbles to shrink