In classical general relativity one can construct configurations with fixed ADM mass but arbitrarily large entropy. These objects collapse into black holes but have more entropy than the area of the resulting black hole. Their interpretation in quantum gravity and in the AdS/CFT duality is an open question.
This topic is also nicely discussed by Don Marolf here and here.
It was great to have Bill Unruh in the audience, whom I had never met in person before.