  A generalized physical model is introduced to describe the impulsive
stimulated scattering (ISS) response of relaxing systems to photothermal
excitation in a periodical grating geometry. The proposed approach starts from
Debye and Havriliak-Negami expressions for both the frequency-dependent heat
capacity, C({\omega}), and thermal expansion coefficient, {\gamma}({\omega}).
Simulations are carried out on glycerol to test and compare the developed
models with the existing semi-empirical model [1]. Debye behavior of the
specific heat capacity is shown to be compatible with a two-temperature
scenario, in which, in addition to the classical, experimentally observable
temperature that characterizes the distribution of the system over vibrational
energy states, a second temperature characterizes the state of the
configurational energy landscape. The models here developed have been applied
for the interpretation of the experimental ISS signals of supercooled glycerol,
illustrating simultaneous and separate assessment of C({\omega}) and
{\gamma}({\omega}) up to sub-100 MHz from thermoelastic transients.
