On the reality of the residual entropy of glasses and disordered crystals: The entropy of mixing

We have previously shown that the assumption that the configurational entropy of a supercooled liquid vanishes at Tg leads to a non-trivial violation of the second law. Here we consider the example of the entropy of mixing. We use as a model system two similar chemical substances which form an ideal solution in a mixed phase. We apply the reasoning of our earlier paper to show that this vanishing would lead to a dilemma; either it violates the second law of thermodynamics, or else it cannot be demonstrated by any conceivable experiment. We show further that the vanishing of the entropy of mixing on kinetic arrest leads to the counter-intuitive result that the chemical potential of each component in an infinitely dilute kinetically arrested (or glassy) solution can equal or the chemical potential of the pure component. The most parsimonious conclusion from these results is that residual entropies are real.