On the Subadditivity of the Entropy on the Sphere
The Journal of Geometric Analysis
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Einav, A. (2015). On the Subadditivity of the Entropy on the Sphere. The Journal of Geometric Analysis https://doi.org/10.1007/s12220-015-9664-9
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 with respect to the entropy. Additionally, we remark about the connection between this inequality and the investigation of the many-body Cercignani’s conjecture.
equivalence of ensembles, entropy, entropic inequalities, transportation distances, Kac’s model
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.
External DOI: https://doi.org/10.1007/s12220-015-9664-9
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255036