Non-additive entropies in ... gravity ?

We present aspects of entropic functionals relatively recently introduced in Physics which are non-additive, in the conventional sense of the word, some of which have a power-law functional form. We use as an example among them, and to be concrete in this work the “Tsallis entropy”, which has, arguably, the simplest functional form. We present some of its properties and speculate about its potential uses in semi-Classical and Quantum Gravity.