  We study the thermodynamics of the strange baryon system using an S-matrix
formulation of statistical mechanics. For this purpose, we employ an existing
coupled-channel study involving $\bar{K} N$, $\pi \Lambda$, and $\pi \Sigma$
interactions in the $S=-1$ sector. A novel method is proposed to extract an
effective phase shift due to the interaction, which can subsequently be used to
compute various thermal observables via a relativistic virial expansion. As an
application of the calculation scheme, we compute the correlation of the net
baryon number with strangeness ($\chi_{BS}$) for an interacting hadron gas. We
show that the S-matrix approach, which entails a consistent treatment of
resonances and naturally incorporates the additional hyperon states which are
not listed by the Particle Data Group, leads to an improved description of the
lattice data over the Hadron Resonance Gas model.
