  In a previous paper, we proposed a probability interpretation for higher
genus amplitudes of BMN (Berenstein-Maldacena-Nastase) strings in a pp-wave
background with infinite negative curvature. This provides a natural definition
of the entropy of a BMN string as the Shannon entropy of its corresponding
probability distribution. We prove a universal upper bound that the entropy
grows at most logarithmically in the strong string coupling limit. We also
study the entropy by numerical methods and discuss some interesting salient
features.
