Partially averaged or resolved distributions of quantum states are measured (or simulated) in diverse branches of Physics, in Chemical Physics and more recently in Biological Physics. Lately they are an output of quantum computations. Surprisal analysis, a blending of information theory and thermodynamics has been extensively used to characterize and compact such distributions. Currently, when coherence between quantum states is of central interest, the algebraic awkwardness of implementing a quantum mechanical procedure of maximal entropy is becoming an issue. We present a novel theoretical approach and its practical computational implementation with special reference to dynamical processes.