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

Pharmacotherapy review: a proposal to improve medication adherence among hypertensive patients

Abstract Pharmacotherapy review is a structured assessment of medicines, which aims to obtain a partnership with patients to achieve drug treatment goals and agreement about drug dosage, as well as when and how the drugs should be administered. The objective was to analyze the influence of pharmacotherapy review, by scheduling drug administration to improve medication adherence among antihypertensive patients. This study was an uncontrolled intervention developed in three distinct stages. The first stage included data collection on the profile of patients and their medications, and a preliminary assessment of medication adherence. In the second stage, the review report was delivered to patients. In the third stage, the results of blood pressure and medication adherence were assessed. The influence of the revision was measured through statistical tests (p<0.05). The study included 40 patients with a mean age of 58.0 (SD:11.3) years; 72.5% were women. Thirty-three (82.5 %) patients required some intervention, after when there was a significant increase in the number of daily doses (p=0.039) and drug intakes (p=0.025). There was a significant increase in the adherence rate, according to both the Morisky-Green test (p<0.001) and self-reported assessment (p=0.004). There was also an improvement in the levels of systolic (p<0.001) and diastolic (p=0.002) blood pressure and in the number of patients with controlled hypertension (p=0.006). The pharmaceutical service enhanced medication adherence and control of systemic blood pressure; however, it increased the complexity of treatment