Initial states of maximal entropy in formal scattering theory

For a precollision state which is not sharply defined, not all details of the dynamics can be obtained by examination of the final state. A version of formal collision theory which takes full advantage of the inherent loss of detail is provided. Only the relevant aspects of the dynamics need then be computed and an explicit identification of the relevant details is provided by a generalized intertwining theorem. Several explicit examples where this point of view can be implemented are worked out.