Charged Rényi entropies and holographic superconductors

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...

Holographic superconductors

It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qua...

Strong converse theorems using Rényi entropies