On the reality of residual entropies of glasses and disordered crystals

We show that the hypothesis that the configurational entropy of a liquid disappears when it is kinetically frozen into a single glass state implies a spontaneous decrease of entropy. We show further that this is not an innocuous exception to the second law that requires a slight modification of that law, but rather implies directly the possibility of an uncompensated conversion of heat to work. We also note that the number of microstates visited in the course of a measurement does not determine the entropy, but rather that this number is always an inconceivably small fraction of the accessible microstates. Various experimental and computational tests of the possible vanishing of configurational entropy on kinetic arrest (e.g., from studies of glass vapor pressure and solubilities, and the coexistence curve between a disordered crystal and the liquid), with the exception of one questionable case, are consistent with the view that it does not vanish. We then show that this result is actually required by the second law. These considerations apply equally to the residual entropy of disordered crystals.