Hydro-climatic and ecological behaviour of the drought of Amazonia in 2005

In 2005, southwestern Amazonia experienced the effects of an intense drought that affected life and biodiversity. Several major tributaries as well as parts of the main river itself contained only a fraction of their normal volumes of water, and lakes were drying up. The consequences for local people, animals and the forest itself are impossible to estimate now, but they are likely to be serious. The analyses indicate that the drought was manifested as weak peak river season during autumn to winter as a consequence of a weak summertime season in southwestern Amazonia; the winter season was also accompanied by rainfall that sometimes reached 25% of the climatic value, being anomalously warm and dry and helping in the propagation of fires. Analyses of climatic and hydrological records in Amazonia suggest a broad consensus that the 2005 drought was linked not to El Niño as with most previous droughts in the Amazon, but to warming sea surface temperatures in the tropical North Atlantic Ocean

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