  A master equation description of the inherent dynamics is used to calculate
the frequency-dependent linear thermo-visco-elastic response functions of a
glass-forming liquid. From the imaginary parts of the isobaric specific heat,
isothermal bulk modulus, and isobaric thermal expansion coefficient, we define
a quantity $\Lambda_{Tp}(\omega)$ with the property that
$\Lambda_{Tp}(\omega)=1$ is equivalent to having a one-parameter description of
the linear thermo-visco-elastic response. This provides an alternative to the
well-known criterion based on the Prigogine-Defay ratio.
