The conditional entropy in the microcanonical ensemble: The quantum lattice

The existence of the conditional entropy in the thermodynamic limit for a class of long range compatible observables operating on a quantum lattice is exhibited for the microcanonical ensemble. This limit is demonstrated first along a special sequence of cubes with a fixed contraction parameter. Properties of the parameter dependent limit are utilized to remove the parameter, and the results are extended to van Hove sequences approximable by cubes.