This prediction for the time-average of the observable A ^ ^ is referred to as its predicted value in the diagonal ensemble, The most important aspect of the diagonal ensemble is that it depends explicitly on the initial state of the system, and so would appear to retain all of the information regarding the preparation of the system. In contrast, the predicted value in the microcanonical ensemble is given by the equally-weighted average over all energy eigenstates within some energy window centered around the mean energy of the system