  We study stationary metastable states(SMS's)using a restricted partition
function formalism. The formalism ensures that SMS free energy exists all the
way to T=0, and remains stable. We introduce the concept of the reality
condition, according to which the entropy $S(T)$ of a set of coupled degrees of
freedom must be non-negative. The entropy crisis, which does not affect
stability, is identified as the violation of the reality condition. We identify
and validate rigorously, using general thermodynamic arguments, the following
general thermodynamic mechanism behind the entropy crisis in SMS. The free
energy $F_{\text{dis}}(T)$ of any SMS must be equal to the T=0 crystal free
energy $E_{0}$ at two different temperatures $T=0,$ and $T=T_{\text{eq}}>0$.
Thus, the stability requires $F_{\text{dis}}(T)$ to possess a maximum at an
intermediate but a strictly positive temperature $T_{\text{K}},$ where the
energy is $E=E_{\text{K}}.$ The SMS branch below $T_{\text{K}}$ gives the
entropy crisis and must be replaced by hand by an ideal glass free energy of
constant energy $E_{\text{K}},$ and vanishing entropy. Hence, $T_{\text{K}}>0$
represents the Kauzmann temperature. The ideal glass energy $E_{\text{K}}$ is
higher than the crystal energy $E_{0}$ at absolute zero, which is in agreement
with the experimenatal fact that the extrapolated energy of a real glass at T=0
is higher than its T=0 crystal energy. We confirm the general predictions by
two exact calculations, one of which is not mean-field. The calculations
clearly show that the notion of SMS is not only not vaccuous, but also not a
consequence of a mean-field analysis. They also show that certain folklore
cannot be substantiated.
