Isentropic evolution of the matter in heavy-ion collisions and the search for the critical endpoint

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.