Study of the thermodynamic properties of hot QCD matter with the CMS experiment

These proceedings summarize recent CMS measurements at the LHC that extract the squared speed of sound, $c_s^2$, of strongly interacting matter at extreme temperatures from the multiplicity dependence of the mean transverse momentum in ultra-central lead-lead (PbPb) collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02\mathrm{T}\mathrm{e}\mathrm{V}$. The analysis yields $c_s^2=0.241\pm 0.002(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.016(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$ at an effective temperature of $T_{\mathrm{e}\mathrm{f}\mathrm{f}}=219\pm 8(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mathrm{M}\mathrm{e}\mathrm{V}$, in good agreement with lattice-QCD calculations. Complementary studies in proton-lead (pPb) collisions are also presented to investigate possible quark-gluon plasma signatures in smaller systems.