  Recollapsing homogeneous and isotropic models present one of the key
ingredients for cyclic scenarios. This is considered here within a quantum
cosmological framework in presence of a free scalar field with, in turn, a
negative cosmological constant and spatial curvature. Effective equations shed
light on the quantum dynamics around a recollapsing phase and the evolution of
state parameters such as fluctuations and correlations through such a turn
around. In the models considered here, the squeezing of an initial state is
found to be strictly monotonic in time during the expansion, turn around and
contraction phases. The presence of such monotonicity is of potential
importance in relation to a long standing intensive debate concerning the
(a)symmetry between the expanding and contracting phases in a recollapsing
universe. Furthermore, together with recent analogous results concerning a
bounce one can extend this monotonicity throughout an entire cycle. This
provides a strong motivation for employing the degree of squeezing as an
alternative measure of (quantum) entropy. It may also serve as a new concept of
emergent time described by a variable without classical analog. The evolution
of the squeezing in emergent oscillating scenarios can in principle provide
constraints on the viability of such models.
