  We study the isentropic evolution of the matter produced in relativistic
heavy-ion collisions for various values of the entropy-per-baryon ratio of
interest for the ongoing and future experimental searches for the critical
endpoint (CEP) in the QCD phase diagram: these includes the current
Beam-Energy-Scan (BES) program at RHIC and the fixed-target collisions foreseen
for the near future at various facilities. We describe the hot-dense matter
through two different effective Lagrangians: the PNJL
(Polyakov-Nambu-Jona-Lasinio) and the PQM (Polyakov-quark-meson) models. We
focus on quantities expected to have a direct experimental relevance: the speed
of sound, responsible for the collective acceleration of the fireball, and the
generalized susceptibilities, connected to the cumulants of the distributions
of conserved charges. In principle, they should affect the momentum spectra and
the event-by-event fluctuations of the yields of identified particles. Taking
realistic values for the initial temperature and the entropy-per-baryon ratio
we study the temporal evolution of the above quantities looking for differences
along isentropic trajectories covering different regions of the QCD phase
diagram, passing far or close to the CEP or even intersecting the first-order
critical line.
