  In this paper, we present a simple proof of a recent result of the second
author which establishes that functional inverse-Santal{\'o} inequalities
follow from Entropy-Transport inequalities. Then, using transport arguments
together with elementary correlation inequalities, we prove these sharp
Entropy-Transport inequalities in dimension 1. We also revisit the proof of the
functional inverse-Santal{\'o} inequalities in the n dimensional unconditional
case using these ideas.
