  We consider nonequilibrium (NEQ) states such as supercooled liquids and
glasses that are described with use of internal variables. We classify the
latter by state-dependent hierarchy of relaxation times to assess their
relevance for irreversible contributions. Given an observation time
{\tau}_{obs}, we determine the window of relaxation times that divide the
internal variables into active and inactive groups, the former playing a
central role in the NEQ thermodynamics. Using this thermodynamics, we determine
(i) a bound on the NEQ entropy and on the residual entropy, and (ii) the nature
of isothermal relaxation of the entropy and the enthalpy in accordance with the
second law. A theory that violates the second law such as the entropy loss view
is shown to be internally inconsistent if we require it to be consistent with
experiments. The inactive internal variables still play an indirect role in
determining the temperature T(t), the pressure P(t), of the system, which
deviate from their external values.
