  Relevant and fundamental concepts of the statistical mechanical theory of
classical liquids are ordinarily introduced in the context of the description
of thermodynamic equilibrium states. This makes explicit reference to
probability distribution functions of \emph{equilibrium} statistical ensembles
(canonical, microcanonical, ...) in the derivation of general and fundamental
relations between inter-particle interactions and measurable macroscopic
properties of a given system. This includes, for instance, expressing the
internal energy and the pressure as functionals of the radial distribution
function, or writing transport coefficients (diffusion constant, linear
viscosity, ...) in terms of integral relations involving both, static and
dynamic auto-correlation functions (density-density, stress-stress, ...). Most
commonly, however, matter is not in thermodynamic equilibrium, and this calls
for the extension of these relations to out-of-equilibrium conditions with the
aim of understanding, for example, the time-dependent transient states during
the process of equilibration, or the aging of glass- and gel-forming liquids
during the formation of non-equilibrium amorphous solid states. In this work we
address this issue from both, a general perspective and an illustrative
concrete application focused on the first principles description of rheological
and viscoelastic properties of glass- and gel-forming liquids.
