  We consider copulas with a given diagonal section and compute the explicit
density of the unique optimal copula which maximizes the entropy. In this
sense, this copula is the least informative among the copulas with a given
diagonal section. We give an explicit criterion on the diagonal section for the
existence of the optimal copula and give a closed formula for its entropy. We
also provide examples for some diagonal sections of usual bivariate copulas and
illustrate the differences between them and the maximum entropy copula with the
same diagonal section.
