We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by L. Bowen and is essentially a special case of his measure entropy theory for actions of sofic groups. In this paper we relate the f-invariant entropy of a finitely generated free group action to the f-invariant entropy of the restricted action of a subgroup. ...

We suggest a duality invariant formula for the entropy and temperature of nonextreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymm...

In this paper we show that the entropy of a cosmological horizon in topological Reissner-Nordström-de Sitter and Kerr-Newman-de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any number of dimension. Furthermore, we find that the entropy of a black hole horizon can also be rewritten in terms of the Cardy-Verl...

String theory is used to compute the microscopic entropy for several examples of black holes in compactifications with N = 2 supersymmetry. Agreement with the Bekenstein-Hawking entropy and the moduli-independent N = 2 area formula is found in all cases.

We analyse an analog of the entropy-power inequality for the weighted entropy. In particular, we discuss connections with weighted Lieb‘s splitting inequality and an Gaussian additive noise formula. Examples and counterexamples are given, for some classes of probability distributions.

It is shown that the E6(6) symmetric entropy formula describing black holes and black strings in D = 5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W (E6). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by ...

In this paper we show that the entropy of de Sitter space with a black hole in arbitrary dimension can be understood using a modified Cardy-Verlinde entropy formula. We also comment on the observer dependence of the de Sitter entropy and make a conjecture about the form of the conformal anomaly in arbitrary dimension.