Tracking the confinement phase transition in the thermodynamic observables of QCD at finite density

It is exciting that the heavy-ion collision experiments are now entering the high baryon density region in the QCD phase diagram, with an increasing number of high-statistics measurements expected in the near future. In this proceeding, we discuss possible signatures of QCD confinement at high density in two specific thermodynamic observables: the isentropic trajectories, and the baryon number fluctuations. For predicting the thermodynamic properties of these observables, new theoretical frameworks are developed for a direct calculation on the QCD equation of state via continuum correlation functions, especially for the confinement aspect via the Polyakov loops and the gluonic background field, which can be useful to tackle the urgently needed high density region, in parallel to experimental studies.