UC Berkeley

We give a broad overview of Gaussian entropy inequalities, discuss their scope, analyze their structure, and introduce novel ones. Our new inequalities highlight the connection between information theoretic and analytical inequalities. We then derive a Gaussian comparison inequality that unites a bulk of pre-existing Gaussian entropy inequalities. We present the equality conditions for the Anantharam-Jog-Nair inequalities, and thus derive equality conditions for a wide class of inequalities including the entropy power inequality, the Zamir-Feder inequality, and the Brascamp-Lieb inequalities. We conclude with a discussion of the extremizers of Forward-Reverse Brascamp-Lieb inequalities.