  The celebrated Otto calculus has established itself as a powerful tool for
proving quantitative energy dissipation estimates and provides with an elegant
geometric interpretation of certain functional inequalities such as the
Logarithmic Sobolev inequality. However, the \emph{local} versions of such
inequalities, which can be proven by means of Bakry-Emery-Ledoux
$\Gamma$-calculus, has not yet been given an interpretation in terms of this
Riemannian formalism. In this short note we close this gap by explaining how
Otto calculus applied to the Schr{\"o}dinger problem yields a variations
interpretation of the local logarithmic Sobolev inequalities, that could
possibly unlock novel class of local inequalities.
