  Neutron star configurations are considered as thermodynamical systems for
which a phase diagram in the angular velocity (Omega) - baryon number (N) plane
is obtained with a dividing line N_{crit}(Omega) for quark core configurations.
Trajectories of neutron star evolution in this diagram are studied for
different scenarios defined by the external torque acting on the star due to
radiation and/or mass accretion. They show a characteristic change in the
rotational kinematics when the star enters the quark core regime. For isolated
pulsars the braking index signal for deconfinement has been studied in its
dependence on the mass of the star. Model calculations of the spin evolution of
accreting low-mass X-ray binaries in the phase diagram have been performed for
different values of the initial magnetic field, its decay time as well as
initial mass and mass accretion rate. Population clustering of these objects at
the line N_{crit}(Omega) in the phase diagram is suggested as an observable
signal for the deconfinement phase transition if it exists for spinnning and
accreting neutron stars.
