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

Qualidade sanitária e fisiológica de sementes de abóbora variedade menina Brasileira.

O trabalho teve como objetivos avaliar e correlacionar a qualidade sanitária e fisiológica de sementes de abóbora, variedade Menina Brasileira (Cucurbita moschata.). Foram avaliados dois lotes de sementes de abóbora produzidas no sistema agroecológico e quatro no sistema convencional, com e sem tratamento químico. Os lotes foram submetidos aos testes de sanidade, seguindo a metodologia do “Blotter test”, com congelamento, germinação e vigor (primeira contagem, índice de velocidade de germinação, envelhecimento acelerado e emergência de plântulas). Os resultados indicaram a separação dos lotes de diferentes origens a partir da qualidade sanitária e fisiológica, onde as maiores incidências de fungos foram observadas nos lotes agroecológicos e o maior potencial fisiológico foi observado nos lotes de origem convencional não tratados. Foram encontrados os fungos Fusarium oxysporum, Alternaria alternata, Cladosporium cucumerinum, Aspergillus niger, Penicillium digitatum, Rhizopus stolonifer e Phoma terrestris. A qualidade sanitária não interferiu na qualidade fisiológica das sementes de abóbora, variedade Menina Brasileira

One-dimensional quantum channel and Hawking radiation of the Kerr and Kerr-Newman black holes

In this paper, we review the one-dimensional quantum channel and investigate Hawking radiation of bosons and fermions in Kerr and Kerr-Newman black holes. The result shows the Hawking radiation can be described by the quantum channel. The thermal conductances are derived and related to the black holes' temperatures.Comment: V2, 12 pages. Typo correcte