Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

Abstract

Abstract:In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein-Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System (IFS) is considered, and we prove that these definitions for topological entropy of IFS's are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an IFS which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

Logical Entropy of Information Sources

“…In the 19th century, Carnot and Clausius diversified the concept of entropy into three main directions—entropy associated with heat engines (where it behaves similar to a thermal charge), statistical entropy, and (according to Boltzmann and Shannon) entropy in communications channels and information security. Thus, the theory of entropy plays a key role in mathematics, statistics, dynamical systems (where complexity is mostly measured by entropy), information theory [ 1 ], chemistry [ 2 ], and physics [ 3 ] (see also [ 4 , 5 , 6 ]).…”

The lower sensitivities and the sensitivities of the Schwarzschild metric near the Schwarzschild black hole

“…These definitions have been deduced via different approaches to the notion of sensitivity. For example in one manner a system is called chaotic if its entropy is positive, and since the entropy has been considered via different viewpoints [2][3][4][5][6][7][8][9][10][11], then we deduce different types of chaotic systems. In the next section we define m functions to evaluate the lower sensitivity of a pseudo-metric on a manifold M of dimension m via a given chart of it.…”