  Understanding cause-effect relationships is a crucial part of the scientific
process. As Bell's theorem shows, within a given causal structure, classical
and quantum physics impose different constraints on the correlations that are
realisable, a fundamental feature that has technological applications. However,
in general it is difficult to distinguish the set of classical and quantum
correlations within a causal structure. Here we investigate a method to do this
based on using entropy vectors for Tsallis entropies. We derive constraints on
the Tsallis entropies that are implied by (conditional) independence between
classical random variables and apply these to causal structures. We find that
the number of independent constraints needed to characterise the causal
structure is prohibitively high such that the computations required for the
standard entropy vector method cannot be employed even for small causal
structures. Instead, without solving the whole problem, we find new Tsallis
entropic constraints for the triangle causal structure by generalising known
Shannon constraints. Our results reveal new mathematical properties of
classical and quantum Tsallis entropies and highlight difficulties of using
Tsallis entropies for analysing causal structures.
