  Under many circumstances many soft and hard materials are present in a
puzzling wealth of non-equilibrium amorphous states, whose properties are not
stationary and depend on preparation. They are often summarized in
unconventional "phase diagrams" that exhibit new "phases" and/or "transitions",
in which the time, however, is an essential variable. This work proposes a
solution to the problem of theoretically defining and predicting these
non-equilibrium phases and their time-evolving phase diagrams, given the
underlying molecular interactions. We demonstrate that these non-equilibrium
phases and the corresponding non-stationary (i.e., aging) phase diagrams can
indeed be defined and predicted using the kinetic perspective of a novel
non-equilibrium statistical mechanical theory of irreversible processes. This
is illustrated with the theoretical description of the transient process of
dynamic arrest into non-equilibrium amorphous solid phases, of an
instantaneously-quenched simple model fluid involving repulsive hard-sphere
plus attractive square well pair interactions.
