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Statistical hadronization models are extremly succesful in describingmeasured ratios of hadrons produced in heavy-ion collisions for a wide range ofbeam energies from SIS to RHIC. Using the idea of statistical hadronization atthe phase boundary within the framework of a recently proposed dynamical modelfor the thermodynamics of fireballs, we establish a relation between theequation of state (EoS) in the partonic phase probed at the phase transitiontemperature T_C and the measured hadron ratios. In this way, the ratios can bepredicted parameter-free. We demonstrate that this framework gives a consistentdescription of conditions both at SPS and RHIC. As the data on dileptonemission from heavy ion collisions give evidence for strong in-mediummodifications of hadronic properties, we schematically investigate thesensitivity of our results to such modifications and qualitatively sketch aconsistent scenario involving such in-medium effects.Comment: 11 pages, 6 figures, accepted for publication in Phys. Rev.

Statistical hadronization as a snapshot of a dynamical fireball evolution