The issue of microstate counting for general black holes in D = 5, N = 2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS2. Furthermore, we show that the considered supergravity theory enjoys a duality invariance which conn...

We derive a high-resolution formula for the quantization and entropy coding approximation quantities for fractional Brownian motion, respective to the supre-mum norm and L p [0, 1]-norm distortions. We show that all moments in the quanti-zation problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremu...

A local formula for the dimension of a superselection sector in Quantum Field Theory is obtained as vacuum expectation value of the exponential of the proper Hamiltonian. In the particular case of a chiral conformal theory, this provides a local analogue of a global formula obtained by Kac and Wakimoto within the context of representations of certain affine Lie algebras. Our formula is model in...

We continue the study of thermodynamics of black holes in de Sitter spaces. In a previous paper (hep-th/0111093), we have shown that the entropy of cosmological horizon in the Schwarzschild-de Sitter solutions and topological de Sitter solutions can be expressed in a form of the Cardy-Verlinde formula, if one adopts the prescription to compute the gravitational mass from data at early or late t...

We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature showing that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extrema...

A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the Dand M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation, and information loss; D-branes as probes of black holes; and the Matrix theory approach to charged a...

We study aspects of d-dimensional black holes with two electric charges, corresponding to fundamental strings with generic momentum and winding on an internal circle. The perturbative α corrections to such black holes and their gravitational thermodynamics are obtained. The latter are derived using the Euclidean approach and the Wald formula for the entropy. We find that the entropy and the cha...

We demonstrate an efficient formula to compute the entropy rate H(μ) of a hidden Markov process with q output symbols where at least one symbol is unambiguously received. Using an approximation to H(μ) to the first N terms we give a O(Nq) algorithm to compute the entropy rate of the hidden Markov model. We use the algorithm to estimate the entropy rate when the parameters of the hidden Markov m...

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa...

We derive the entropy formula for the linear heat equation on general Riemannian manifolds and prove that it is monotone non-increasing on manifolds with nonnegative Ricci curvature. As applications, we study the relation between the value of entropy and the volume of balls of various scales. The results are simpler version, without Ricci flow, of Perelman’s recent results on volume non-collaps...