We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes’ inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the nonnegative matrices in the framework of matrix ana...

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT per...

Hawking radiation is viewed as a tunnelling process. In this way the effect of selfgravitation gives rise to semiclassical corrections to the entropy of the (2 + 1) BTZ black hole. The modified entropy, due to specific modelling of the self-gravitation effect, of the (2 + 1) BTZ black hole is evaluated. To first order in ω which is a shell of energy radiated outwards the event horizon of the BT...

We revisit the problem of estimating Renyi Entropy from samples, focusing on the important case of collision entropy. With n samples we approximate the collision entropy of X within an additive factor of O ( 2 log 1 2 (1/ ) ) with probability 1− , where ∆ is a known (a priori) upper bound on the difference between Renyi entropies of X of order 2 and 3 respectively. In particular, we simplify an...

We study how to extract randomness from a C-interleaved source, that is, a source comprised of C independent sources whose bits or symbols are interleaved. We describe a simple approach for constructing such extractors that yields: • For some δ > 0, c > 0, explicit extractors for 2-interleaved sources on {0, 1} when one source has min-entropy at least (1 − δ)n and the other has min-entropy at l...

The measure-theoretic definition of Kullback-Leibler relative-entropy (KL-entropy) plays a basic role in the definitions of classical information measures. Entropy, mutual information and conditional forms of entropy can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. These measure-theoretic defi...

the polarimetric entropy and the alpha angle are two important parameters for analyzing polarimetric synthetic aperture radar data. they demonstrate the degree of randomness in the polarization of the received signal and scattering mechanism of scatterers respectively. recently, there has been an increasing interest in compact polarimetry due to its advantages in comparison with full polarimetr...

We prove the existence of an open and dense subset of maps f 2 Diff 1 ! (S 2) which have positive topological entropy. It follows that these maps have innnitely many hyperbolic periodic points and an exponential growth rate of hyperbolic periodic points. The proof is an application of Pixton's theorem. Topological entropy characterizes the total exponential orbit complexity of a map with a sing...

We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bou...

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[̺] = −Tr ( ̺ ln̺ ) of a density matrix ̺123 on the product of three Hilbert spaces satisfies S[̺123] − S[̺23] ≤ S[̺12] − S[̺2]. We strengthen this to S[̺123]−S[̺12] ≤ ∑ α n ( S[̺ 23 ]−S[̺α 2 ] ) , where the n are weights and the ̺ 23 are partitions of ̺23. Correspondingly, there is a...