  We have recently applied the second law to an isolated system, consisting of
a system {\Sigma} such as a glass surrounded by an extremely large medium
{\Sigma}, to show that the instantaneous temperature T(t), thermodynamic
entropy S(T_0,t) and enthalpy H(T_0,t) of {\Sigma} decrease in any isothermal
relaxation towards their respective equilibrium values under isobaric cooling.
The Gibbs statistical entropy also conforms to the above relaxation behavior in
a glass, which however is contrary to the conjecture by Gupta, Mauro and
coworkers that the glass transition and the structural relaxation are inverse
processes. However, they do not establish that the entropy loss during the
glass transition is accompanied by a concomitant entropy gain of the medium to
maintain the second law. They use a novel statistical formulation of entropy
based on several conjectures such as it being zero for a microstate, but do not
compare its behavior with the thermodynamic entropy. The formulation is
designed to show the entropy loss. Its subsequent rise not only contradicts our
result but also implies that the glass during relaxation must have a negative
absolute temperature. To understand these puzzling results and the above
conjecture, we have carried out a critical evaluation of their unconventional
approach. We find that the inverse conjecture is neither supported by their
approach nor by the second law. The zero-entropy microstate conjecture is only
consistent with S(T_0,t)\equiv 0 at all temperatures, not just at absolute zero
and is found to have no scientific merit. We show that the maximum entropy gain
of the medium during the glass transition invalidates the entropy loss
conjecture. After pointing out other misleading, confusing and highly
exaggerated statements in their work, we finally conclude that their
unconventional statistical approach and computational scheme are not
appropriate for glasses.
