  We follow the consequences of internal equilibrium in non-equilibrium systems
that has been introduced recently [Phys. Rev. E 81, 051130 (2010)] to obtain
the generalization of Maxwell's relation and the Clausius-Clapeyron relation
that are normally given for equilibrium systems. The use of Jacobians allow for
a more compact way to address the generalized Maxwell relations; the latter are
available for any number of internal variables. The Clausius-Clapeyron relation
in the subspace of observables show not only the non-equilibrium modification
but also the modification due to internal variables that play a dominant role
in glasses. Real systems do not directly turn into glasses (GL) that are frozen
structures from the supercooled liquid state L; there is an intermediate state
(gL) where the internal variables are not frozen. Thus, there is no single
glass transition. A system possess several kinds of glass transitions, some
conventional (L \rightarrow gL; gL\rightarrow GL) in which the state change
continuously and the transition mimics a continuous or second order transition,
and some apparent (L\rightarrow gL; L\rightarrow GL) in which the free energies
are discontinuous so that the transition appears as a zeroth order transition,
as discussed in the text. We evaluate the Prigogine-Defay ratio {\Pi} in the
subspace of the observables at these transitions. We find that it is normally
different from 1, except at the conventional transition L\rightarrow gL, where
{\Pi}=1 regardless of the number of internal variables.
