  We investigate the possibility of distinguishing among different causal
relations starting from a limited set of marginals. Our main tool is the notion
of adhesivity, that is, the extension of probability or entropies defined only
on subsets of variables, which provides additional independence constraints
among them. Our results provide a criterion for recognizing which causal
structures are indistinguishable when only limited marginal information is
accessible. Furthermore, the existence of such extensions greatly simplifies
the characterization of a marginal scenario, a result that facilitates the
derivation of Bell inequalities both in the probabilistic and entropic
frameworks, and the identification of marginal scenarios where classical,
quantum, and postquantum probabilities coincide.
