Rényi entropies and area operator from gravity with Hayward term

Swiveled Rényi entropies

This paper introduces “swiveled Rényi entropies” as an alternative to the Rényi entropic quantities put forward in [Berta et al., Physical Review A 91, 022333 (2015)]. What distinguishes the swiveled Rényi entropies from the prior proposal of Berta et al. is that there is an extra degree of freedom: an optimization over unitary rotations with respect to particular fixed bases (swivels). A conse...

Joint Range of Rényi Entropies

The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied.

Rényi entropies and nonlinear diffusion equations

Since their introduction in the early sixties [20], the Rényi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between Rényi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in s...

Strong converse theorems using Rényi entropies

On Rényi and Tsallis entropies and divergences for exponential families

Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both Rényi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that Rényi and Tsallis entropies c...