This is an announcement for the paper "Relative entropy of cone measures and $L_p$ centroid bodies" by Grigoris Paouris and Elisabeth M. Werner. Abstract: Let $K$ be a convex body in $\mathbb R^n$. We introduce a new affine invariant, which we call $\Omega_K$, that can be found in three different ways: as a limit of normalized $L_p$-affine surface areas, as the relative entropy of the cone measure of $K$ and the cone measure of $K^\circ$, as the limit of the volume difference of $K$ and $L_p$-centroid bodies. We investigate properties of $\Omega_K$ and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show a "information inequality" for convex bodies. Archive classification: math.FA Mathematics Subject Classification: 52A20, 53A15 The source file(s), PaourWern.tex: 116056 bytes, is(are) stored in gzipped form as 0909.4361.gz with size 27kb. The corresponding postcript file has gzipped size 188kb. Submitted from: elisabeth.werner@case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0909.4361 or http://arXiv.org/abs/0909.4361 or by email in unzipped form by transmitting an empty message with subject line uget 0909.4361 or in gzipped form by using subject line get 0909.4361 to: math@arXiv.org.