In this talk I shall discuss how the S-matrix formalism can be applied to study the thermal properties of interacting hadrons.
The approach allows a consistent treatment of broad resonances and purely repulsive channels, while correctly implementing the constraints from the chiral perturbation theory. This provides a useful framework for identifying the limitations of the Hadron Resonance Gas model and for incorporating additional effects from hadron physics to reliably describing the thermal medium.
As an application I study the pion-nucleon system and demonstrate how the natural implementation of the repulsive forces can help to better understand the lattice QCD result on the baryon electric charge correlation.
Lastly, I discuss some recent progress in extending the analysis to a coupled-channel system of hyperons.