  The assumption of local realism in a Bell locality scenario imposes
non-trivial conditions on the Shannon entropies of the associated probability
distributions, expressed by linear entropic Bell inequalities. In principle,
these entropic inequalities provide necessary but not sufficient criteria for
the existence of a local hidden variable model reproducing the correlations,
as, for example, the paradigmatic nonlocal PR-box is entropically not different
from a classically correlated box. In this paper we show that for the n-cycle
scenario, entropic inequalities completely characterize the set of local
correlations. In particular, every nonsignalling box which violates the CHSH
inequality -- including the PR-box -- can be locally modified so that it also
violates the entropic version of CHSH inequality. As we show, any nonlocal
probabilistic model when appropriately mixed with a local model, violates an
entropic inequality, thus evidencing a very peculiar kind of nonlocality. As
the n-cycle captures equally well both the notion of local realism introduced
by Bell and that of noncontextuality presented by the Kochen-Specker theorem,
the results are also valid for noncontextuality scenarios.
