Cumulants: it's not what you think

Cumulants of baryon number are given considerable attention in analyses of heavy-ion collision experiments as possible signatures of the QCD critical point. In this talk, I will show that the values of the lowest three cumulants can also be utilized to recover information about the incompressibility, the speed of sound, and their logarithmic derivatives. I will then discuss the possible influence of the nuclear liquid-gas phase transition on the measured values of the cumulants.