A note on black hole entropy, area spectrum, and evaporation

We argue that a process where a fuzzy space splits in two others can be used to explain the origin of the black hole entropy, and why a "generalized second law of thermodynamics" appears to hold in the presence of black holes. We reach the Bekenstein-Hawking formula from the count of the microstates of a black hole modeled by a fuzzy space. In this approach, a discrete area spectrum for the black hole, which becomes increasingly spaced as the black hole approaches the Planck scale, is obtained. We show that, as a consequence of this, the black hole radiation becomes less and less entropic as the black hole evaporates, in a way that some information about its initial state could be recovered.Comment: 4 pages, 2 figure

Generalising the logistic map through the qq-product

We investigate a generalisation of the logistic map as $x_{n+1}=1-ax_{n}\otimes_{q_{map}} x_{n}$ ($-1 \le x_{n} \le 1$, $0<a\le2$) where $\otimes_q$ stands for a generalisation of the ordinary product, known as $q$-product [Borges, E.P. Physica A {\bf 340}, 95 (2004)]. The usual product, and consequently the usual logistic map, is recovered in the limit $q\to 1$, The tent map is also a particular case for $q_{map}\to\infty$. The generalisation of this (and others) algebraic operator has been widely used within nonextensive statistical mechanics context (see C. Tsallis, {\em Introduction to Nonextensive Statistical Mechanics}, Springer, NY, 2009). We focus the analysis for $q_{map}>1$ at the edge of chaos, particularly at the first critical point $a_c$, that depends on the value of $q_{map}$. Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at $a_c(q_{map})$, and connections with nonextensive statistical mechanics are explored.Comment: 12 pages, 23 figures, Dynamics Days South America. To be published in Journal of Physics: Conference Series (JPCS - IOP