Based on a diffusion-like master equation we propose a formula using the Bregman divergence for measuring entropic distance in terms of different non-extensive entropy expressions. We obtain the non-extensivity parameter range for a universal approach to the stationary distribution by simple diffusive dynamics for the Tsallis and the Kaniadakis entropies, for the Hanel–Thurner generalization, a...

Abstract For models with several time-dependent components generalized entropies can be defined. This is shown for the Bianchi type IX model. We first derive the Cardy-Verlinde formula under the assumption that the first law of thermodynamics is valid. This leads to an explicit expression of the total entropy associated with this type of universes. Assuming the validity of the Cardy entropy for...

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use Fisher-Hartwig formula, as well as the recent results concerning the asymp-totics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in ...

In nongravitational quantum field theory, the entanglement entropy across a surface depends on the short-distance regularization. Quantum gravity should not require such regularization, and it has been conjectured that the entanglement entropy there is always given by the black hole entropy formula evaluated on the entangling surface. We show that these statements have precise classical counter...

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy ...

We consider the brane universe in the bulk background of the topological AdSSchwarzschild black holes, where the brane tension takes larger value than the finetunned value. The resulting universe is radiation dominated and has positive cosmological constant. We obtain the associated cosmological Cardy formula and the CardyVerlinde formula. We also derive the Hubble and the Bekenstein entropy bo...