  For Euclidean pure point diffractive Delone sets of finite local complexity
and with uniform patch frequencies it is well known that the patch counting
entropy computed along the closed centred balls is zero. We consider such sets
in the setting of sigma-compact locally compact Abelian groups and show that
the topological entropy of the associated Delone dynamical system is zero. For
this we provide a suitable version of the variational principle. We furthermore
construct counterexamples, which show that the patch counting entropy of such
sets can be non-zero in this context. Other counterexamples will show that the
patch counting entropy of such a set can not be computed along a limit and even
be infinite in this setting.
