On the reality of the residual entropies of glasses and disordered crystals: counting microstates, calculating fluctuations, and comparing averages.

In the course of an on-going debate on whether glasses or disordered crystals should have zero entropy at 0 K, i.e., whether the "residual entropy" assigned to them by calorimetric measurements is real, the view has been expressed by some who hold the zero entropy view that to measure entropy, all or an appreciable number of the microstates that contribute to the entropy must be visited. We show here that the entropy calculated on the basis of the number of microstates visited during any conceivable time of measurement would be underestimated by at least 20 orders of magnitude. We also examine and refute the claim that an ensemble average for glassy systems, which predicts a finite residual entropy, also predicts physically impossible properties. We conclude that calorimetrically measured residual entropies are real.