Recently Leutheusser and Liu identified an emergent algebra of Type III_1 in the operator algebra of N=4 super Yang-Mills theory for large N. Here we describe some 1/N corrections to this picture and show that the emergent Type III_1 algebra becomes an algebra of Type II_infty. The Type II_infty algebra is the crossed product of the Type III_1 algebra by its modular automorphism group. In the context of the emergent Type II_infty algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state.
This is somewhat analogous to entropy in classical physics.