Residual entropy and structural disorder in glass: A two-level model and a review of spatial and ensemble vs. temporal sampling

As a contribution to the residual entropy debate for glasses, we have made simulations to compare the configurational entropies of a two-level system as calculated from either classical or statistical thermodynamics under equilibrium and nonequilibrium conditions. Upon cooling the latter entropies become greater than the former so that the real residual entropy is greater than the calorimetrically estimated value. We also find that a new equivalent transformation can precisely convert the value of the calorimetric entropy into that of the statistical thermodynamics in our model. New insights on configurational entropy are obtained in terms of ‘structural degeneracy’ originating from microscopic structural disorder and of macroscopic ‘thermodynamic degeneracy’ related to the number of microstates included in the most probable macrostate. We refute claims against the ‘conventional’ view as related to causality and ergodic theory. We also defend the concept of ‘spatial sampling’ in entropy matters in addition to the traditional ‘ensemble’ and ‘time’ samplings. We conclude that the non-zero values of residual entropies do exist and have clear physical and chemical meanings in real crystals and glasses.