  Motivated by the recent developments about the Hartle-Hawking wave function
associated to black holes, we formulate an entropy functional on the moduli
space of Calabi-Yau compactifications. We find that the maximization of the
entropy is correlated with the appearance of asymptotic freedom in the
effective field theory. The points where the entropy is maximized correspond to
points on the moduli which are maximal intersection points of walls of marginal
stability for BPS states. We also find an intriguing link between extremizing
the entropy functional and the points on the moduli space of Calabi-Yau
three-folds which admit a `quantum deformed' complex multiplication.
