Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio

Boundary Conditions for Interacting Membranes

We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.Comment: 36 pages, latex, v2 minor typos correcte

Thermic effect of a meal and appetite in adults: an individual participant data meta-analysis of meal-test trials

Background: Thermic effect of a meal (TEF) has previously been suggested to influence appetite. Objective: The aim of this study was to assess whether there is an association between appetite and TEF. Second, to examine whether protein intake is associated with TEF or appetite. Design: Individual participant data (IPD) meta-analysis on studies were performed at the Department of Nutrition, Exercise and Sports, University of Copenhagen, Denmark. Five randomized meal-test studies, with 111 participants, were included. The included studies measured energy expenditure (EE) in respiration chambers and pre- and postprandial appetite sensations using Visual Analog Scales (VAS). The primary meta-analysis was based on a generic-inverse variance random-effects model, pooling individual study Spearman's correlation coefficients, resulting in a combined r-value with 95% confidence interval (95% CI). The I2 value quantifies the proportion (%) of the variation in point estimates due to among-study differences. Results: The IPD meta-analysis found no association between satiety and TEF expressed as the incremental area under the curve (TEFiAUC) (r=0.06 [95% CI −0.16 to 0.28], P=0.58; I2=15.8%). Similarly, Composite Appetite Score (CAS) was not associated with TEFiAUC (r=0.08 [95% CI −0.12 to 0.28], P = 0.45; I2=0%). Posthoc analyses showed no association between satiety or CAS and TEF expressed as a percentage of energy intake (EI) (P>0.49) or TEF expressed as a percentage of baseline EE (P>0.17). When adjusting for covariates, TEFiAUC was associated with protein intake (P=0.0085). Conclusions: This IPD meta-analysis found no evidence supporting an association between satiety or CAS and TEF at protein intakes ∼15 E% (range 11–30 E%)