  We take up from a library of 12 galaxy clusters featuring extended X-ray
observations of their Intra Cluster Plasma (ICP), analyzed with our
entropy-based Supermodel. Its few intrinsic parameters - basically, the central
level and the outer slope of the entropy profile - enable us to uniformly
derive not only robust snapshots of the ICP thermal state, but also the
'concentration' parameter marking the age of the host dark matter halo. We test
these profiles for consistency with numerical simulations and observations. We
find the central and the outer entropy to correlate, so that these clusters
split into two main classes defined on the basis of low (LE) or high (HE)
entropy conditions prevailing throughout the ICP. We also find inverse
correlations between the central/outer entropy and the halo concentration. We
interpret these in terms of mapping the ICP progress on timescales around 5 Gyr
toward higher concentrations, under the drive of the dark matter halo
development. The progress proceeds from HEs to LEs, toward states of deeper
entropy erosion by radiative cooling in the inner regions, and of decreasing
outer entropy production as the accretion peters out. We propose these radial
and time features to constitute a cluster Grand Design, that we use here to
derive a number of predictions. For HE clusters we predict sustained outer
temperature profiles. For LEs we expect the outer entropy ramp to bend over,
hence the temperature decline to steepen at low z; this feature goes together
with an increasing turbulent support, a condition that can be directly probed
with the SZ effect.

Cosmology and Nongalactic Astrophysics