In the vicinity of the QCD phase boundary, the thermodynamic pressure receives contributions from a regular component Pr and a non-analytic component Ps. Pr describes the bulk properties of the QCD thermodynamics, whereas Ps carries information on chiral criticality. We discuss the computation of Pr in the hadronic phase within the S-matrix formulation of statistical mechanics, and the determination of Ps using high-order cumulants of net baryon number fluctuations. We show that the S-matrix approach provides a consistent description to both the lattice QCD results on the baryon electric charge correlation and on the proton production yield in heavy ion collisions at the LHC. In addition, it is suggested that chiral criticality is reflected in the energy dependence of certain ratios of net baryon number fluctuations.