Collision experiments with partial resolution of final states: Maximum entropy procedure and surprisal analysis

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Abstract
The application of the maximal entropy approach as a dynamical procedure to collisions when there is incomplete resolution of the final states is discussed. The major objective is to provide a collision theoretic foundation for the phenomenological procedure of surprisal analysis which is applied to heavy-ion induced reactions in a companion paper. A reduced description where during the entire time evolution the degree of detail is commensurate with that available for the analysis of the final state is introduced. An exact equation of motion, in the form of a continuity equation, is derived for the reduced description. The most notable feature of the equation is the inherent presence of a dissipative term. Because of the finite duration of the collision, the final reduced distribution need not, however, be fully relaxed. It is shown it is possible to characterize the deviance from the statistical limit in terms of time-dependent constants of the motion. The post-collision measure of this deviance is the surprisal. The significance of the (time-independent) constraints, identified by surprisal analysis of experimental results, is discussed and the use of sum rules as a practical route to the identification of such constraints is noted. The formulation of the approach as a sophisticated statistical theory capable of representing direct reactions is discussed in the appendix. The variational character of the procedure of maximal entropy is also noted therein as a route to approximate descriptions.