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[abridged] The equilibria of the intracluster plasma (ICP) and of thegravitationally dominant dark matter (DM) are governed by the hydrostatic andthe Jeans equation. Jeans, with the DM `entropy' set to K ~ r^\alpha and \alpha~ 1.25 - 1.3 applying from groups to rich clusters, yields our radial\alpha-profiles. In the ICP the entropy run k(r) is mainly shaped by shocks, assteadily set by supersonic accretion of gas at the cluster boundary, andintermittently driven from the center by merging events or by AGNs; theresulting equilibrium is described by the exact yet simple formalismconstituting our ICP Supermodel. With a few parameters, this accuratelyrepresents the runs of density n(r) and temperature T(r) as required by recentX-ray data on surface brightness and spectroscopy for both cool core (CC) andnon cool core (NCC) clusters; the former are marked by a middle temperaturepeak, whose location is predicted from rich clusters to groups. The Supermodelinversely links the inner runs of n(r) and T(r), and highlights their centralscaling with entropy n_c ~ k_c^-1 and T_c ~ k_c^0.35, to yield radiativecooling times t_c ~ 0.3 (k_c/15 keV cm^2)^1.2 Gyr. We discuss the stability ofthe central values so focused either in CC and NCC clusters. From theSupermodel we derive as limiting cases the classic polytropic \beta-models, andthe `mirror' model with T(r) ~ \sigma^2(r) suitable for NCC and CC clusters,respectively; these highlight how the ICP temperature T(r) tends to mirror theDM velocity dispersion \sigma^2(r) away from entropy injections. Finally, wediscuss how the Supermodel connects information derived from X-ray andgravitational lensing observations.

Galaxy Clusters, a Novel Look at Diffuse Baryons Withstanding Dark Matter Gravity