Single-order-parameter description of glass-forming liquids: A   one-frequency test
  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. 
Niels L. Ellegaard, Tage Christensen, Peder Voetmann Christiansen,   Niels Boye Olsen, Ulf R. Pedersen, Thomas B. Schr{\o}de...