  We propose a unifying picture where the notion of generalized entropy is
related to information theory by means of a group-theoretical approach. The
group structure comes from the requirement that an entropy be well defined with
respect to the composition of independent systems, in the context of a recently
proposed generalization of the Shannon-Khinchin axioms. We associate to each
member of a large class of entropies a generalized information measure,
satisfying the additivity property on a set of independent systems as a
consequence of the underlying group law. At the same time, we also show that
Einstein's likelihood function naturally emerges as a byproduct of our
informational interpretation of (generally nonadditive) entropies. These
results confirm the adequacy of composable entropies both in physical and
social science contexts.
