  Thermo-viscoelastic linear-response functions are calculated from the master
equation describing viscous liquid inherent dynamics. From the imaginary parts
of the frequency-dependent isobaric specific heat, isothermal compressibility,
and isobaric thermal expansion coefficient, we define a "linear dynamic
Prigogine-Defay ratio" with the property that if this quantity is unity atone
frequency, then it is unity at all frequencies. This happens if and only if
there is a single-order-parameter description of the thermo-viscoelastic linear
responses via an order parameter (which may be non-exponential in time).
Generalizations to other cases of thermodynamic control parameters than
temperature and pressure are treated in an Appendix.
