  A new canonical divergence is put forward for generalizing an
information-geometric measure of complexity for both, classical and quantum
systems. On the simplex of probability measures it is proved that the new
divergence coincides with the Kullback-Leibler divergence, which is used to
quantify how much a probability measure deviates from the non-interacting
states that are modeled by exponential families of probabilities. On the space
of positive density operators, we prove that the same divergence reduces to the
quantum relative entropy, which quantifies many-party correlations of a quantum
state from a Gibbs family.
