Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

60,000 years of interactions between Central and Eastern Africa documented by major African mitochondrial haplogroup L2

Mitochondrial DNA (mtDNA) haplogroup L2 originated in Western Africa but is nowadays spread across the entire continent. L2 movements were previously postulated to be related to the Bantu expansion, but L2 expansions eastwards probably occurred much earlier. By reconstructing the phylogeny of L2 (44 new complete sequences) we provide insights on the complex net of within-African migrations in the last 60 thousand years (ka). Results show that lineages in Southern Africa cluster with Western/Central African lineages at a recent time scale, whereas, eastern lineages seem to be substantially more ancient. Three moments of expansion from a Central African source are associated to L2: (1) one migration at 70-50 ka into Eastern or Southern Africa, (2) postglacial movements (15-10 ka) into Eastern Africa; and (3) the southward Bantu Expansion in the last 5 ka. The complementary population and L0a phylogeography analyses indicate no strong evidence of mtDNA gene flow between eastern and southern populations during the later movement, suggesting low admixture between Eastern African populations and the Bantu migrants. This implies that, at least in the early stages, the Bantu expansion was mainly a demic diffusion with little incorporation of local populations.

Extensive admixture and selective pressure across the Sahel Belt

Genome-wide studies of African populations have the potential to reveal powerful insights into the evolution of our species, as these diverse populations have been exposed to intense selective pressures imposed by infectious diseases, diet, and environmental factors. Within Africa, the Sahel Belt extensively overlaps the geographical center of several endemic infections such as malaria, trypanosomiasis, meningitis, and hemorrhagic fevers. We screened 2.5 million single nucleotide polymorphisms in 161 individuals from 13 Sahelian populations, which together with published data cover Western, Central, and Eastern Sahel, and include both nomadic and sedentary groups. We confirmed the role of this Belt as a main corridor for human migrations across the continent. Strong admixture was observed in both Central and Eastern Sahelian populations, with North Africans and Near Eastern/Arabians, respectively, but it was inexistent in Western Sahelian populations. Genome-wide local ancestry inference in admixed Sahelian populations revealed several candidate regions that were significantly enriched for non-autochthonous haplotypes, and many showed to be under positive selection. The DARC gene region in Arabs and Nubians was enriched for African ancestry, whereas the RAB3GAP1/LCT/MCM6 region in Oromo, the TAS2R gene family in Fulani, and the ALMS1/NAT8 in Turkana and Samburu were enriched for non-African ancestry. Signals of positive selection varied in terms of geographic amplitude. Some genomic regions were selected across the Belt, the most striking example being the malaria-related DARC gene. Others were Western-specific (oxytocin, calcium, and heart pathways), Eastern-specific (lipid pathways), or even population-restricted (TAS2R genes in Fulani, which may reflect sexual selection).

Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\'enyi relative entropy formula.