We poorly understand the macroscopic properties of complex fluids and of
amorphous bodies in general. This is mainly due to the interplay between
phenomena at different levels and length-scales. In particular, it is not
necessarily true that the microscopic level (dominated by direct interactions)
coincides with the level where the continuum description comes into play. This
is typically the case in the presence of structural inhomogeneities which are
inherent to all structurally disordered states of matter below close packing.
As a consequence, the macroscopic response to external fields of either fluid
or arrested disordered states is not well understood. In order to disentangle
this complexity, in this work we build upon a simple yet seemingly powerful
concept. This can be summarized as follows: the mesoscopic length-scale of
structural inhomogeneities is assumed to be the characteristic length-scale of
the effective building blocks, while the degrees of freedom of the primary
particles are integrated out. Theoretical results are derived, in the present
work, for the macroscopic response of fluid and dynamically arrested model
colloidal states in fields of shear. The predictions of the coarse-grained
theories and the applicability of the principle are tested in comparison with
original simulation and experimental data
