  Causal structures give us a way to understand the origin of observed
correlations. These were developed for classical scenarios, but quantum
mechanical experiments necessitate their generalisation. Here we study causal
structures in a broad range of theories, which include both quantum and
classical theory as special cases. We propose a method for analysing
differences between such theories based on the so-called measurement entropy.
We apply this method to several causal structures, deriving new relations that
separate classical, quantum and more general theories within these causal
structures. The constraints we derive for the most general theories are in a
sense minimal requirements of any causal explanation in these scenarios. In
addition, we make several technical contributions that give insight for the
entropic analysis of quantum causal structures. In particular, we prove that
for any causal structure and for any generalised probabilistic theory, the set
of achievable entropy vectors form a convex cone.
