We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

Exploiting a recently constructed target space action for the exact string black hole, logarithmic corrections to the leading order entropy are studied. There are contributions from thermal fluctuations and from corrections due to α > 0 which for the microcanonical entropy appear with different signs and therefore may cancel each other, depending on the overall factor in front of the action. Fo...

We compute the spectrum of quarter BPS dyons in freely acting ZZ2 and ZZ3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the e...

We prove that Yuzvinskii’s entropy addition formula can not be extended for the action of certain finitely generated nonamenable groups. 1991 AMS CLASSIFICATION NUMBERS: 22D40, 58F03

We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem 1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li–Yau’s gradient estimate. As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also show that the equalit...

In this letter, we compute the corrections to the Cardy-Verlinde formula of d−dimensional Schwarzschild black hole. These corrections stem from the generalized uncertainty principle. Then we show, one can taking into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator L 0 and the central charge c.

We propose a formula for the degeneracy of quarter BPS dyons in a class of CHL models. The formula uses a modular form of a subgroup of the genus two modular group Sp(2, ZZ). Our proposal is S-duality invariant and reproduces correctly the entropy of a dyonic black hole to first non-leading order for large values of the charges.

A fundamental theme in holomorphic dynamics is that the local geometry of parameter space (e.g. the Mandelbrot set) near a parameter reflects the geometry of the Julia set, hence ultimately the dynamical properties, of the corresponding dynamical system. We establish a new instance of this phenomenon in terms of entropy. Indeed, we prove an “entropy formula” relating the entropy of a polynomial...

We use holographic techniques to calculate the first thermal correction to the entanglement entropy of a cap-like region of a CFT defined on a sphere, successfully reproducing the field theory result. Since this is an order-one correction to the entropy in the large-N expansion, quantum corrections to the holographic entanglement entropy formula are essential. The bulk calculation is made tract...

In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin.