Since the introduction of entropic regularization to optimal transport, several works investigating its bias as well
as statistical properties have been carried out (debiasing, statistical complexity ..) In this presentation, I will discuss
the various implications of the very definition of entropy: discrete, continuous, semi-discrete and debiased. The first part
of the talk will be dedicated to comparing these formulations (+barycenters) for Gaussian measures. In the second part I will
present generalizations of closed form formulae and some potential conjectures for unbalanced OT (with/and without entropy) as well
as multi-marginal OT.