  We introduce a family of equations of state (EoS) for hybrid neutron star
(NS) matter that is obtained by a two-zone parabolic interpolation between a
soft hadronic EoS at low densities and a stiff quark matter EoS with color
superconductivity at high densities within a finite region of baryonic chemical
potentials $\mu_B^h < \mu_B < \mu_B^q$. We consider two scenarios corresponding
to a cross-over and a strong first-order transition between quark and hadron
phases considered at finite and zero temperatures. This allows us to analyze
the effects of finite entropy on the EoS and mass-radius relation of NS. We
demonstrate that the formation of a color superconducting state of quark matter
drives the evolution of matter in supernovae explosions under the condition of
entropy conservation to higher temperatures than in the case of deconfinement
to normal quark matter. Within the presented hybrid EoS scenario, regions of
the QCD phase diagram may be accessible to supernovae and NS mergers that can
be reached also in terrestrial experiments with relativistic heavy ion
collisions.
