Bulk medium properties of heavy-ion collisions from the beam energy scan with a multistage hydrodynamic model

We introduce a method to reconstruct full rapidity distributions of charged particle multiplicity and net proton yields, crucial for constraining the longitudinal dynamics of nuclear matter created in the beam energy scan program. Employing rapidity distributions within a multistage hydrodynamic model calibrated for Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=7.7-200$GeV, we estimate the total energy and baryon number deposited into the collision fireball, offering insights into initial dynamics and the identification of nuclear remnants. We explore the potential of rapidity-dependent measurements in probing equations of state at finite chemical potentials. Furthermore, we compare the freeze-out parameters derived from both hydrodynamics and thermal models, highlighting that the parameters extracted via thermal models represent averaged properties across rapidities.