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

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

Weak phenotypic reversion of ivermectin resistance in a field resistant isolate of Haemonchus contortus by verapamil

Recent advances in anthelmintic resistant phenotype reversion by Pgp modulating drugs in ruminant nematodes indicate that this can be a useful tool to helminth control. The aim of the present study was to evaluate the efficacy of ivermectin (IVM) in combination with verapamil (VRP), in oil or water-based vehicle, against an IVM-resistant field isolate of Haemonchus contortus through a larval migration assay and experimental infection trial. In the in vitro assay was observed a phenotypic reversion of H. contortus resistance to ivermectin at a high concentration of VRP, increasing IVM efficacy from 53.1% to 94.3. In the in vivo trial, IVM + VRP demonstrated 36.02% efficacy compared to the 7.75% of IVM alone. The vehicle formulation showed no influence in efficacy. These are the first results demonstrating the effect of VRP as a partial IVM-resistance phenotype reverser in a field isolate of IVM-resistant H. contortus experimentally inoculated in sheep