On the Subadditivity of the Entropy on the Sphere
Change log
Authors
Abstract
We present a refinement of a known entropic inequality on the sphere, finding suitable conditions under which the uniform probability measure on the sphere behaves asymptomatically like the Gaussian measure on RN$$\mathbb {R}^N$$ with respect to the entropy. Additionally, we remark about the connection between this inequality and the investigation of the many-body Cercignani’s conjecture.
Description
Journal Title
The Journal of Geometric Analysis
Conference Name
Journal ISSN
1050-6926
1559-002X
1559-002X
Volume Title
Publisher
Springer Nature
Publisher DOI
Rights and licensing
Except where otherwised noted, this item's license is described as http://www.rioxx.net/licenses/all-rights-reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/L002302/1)
We would like to greatly thank Eric Carlen for many discussions and insights on key ideas all along the progression of this work, without which this paper would never have seen the light of day. We would also like to offer our gratitude to Nathael Gozlan for providing us with a reference for the “distorted” HWI inequality we use in Sect. 3, and Clément Mouhot for several discussions on the present results. The author was supported by EPSRC Grant EP/L002302/1.