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The nuclear liquid-gas transition at normal nuclear densities, $n \sim n_0 =0.16$ fm$^{-3}$, and small temperatures, $T \sim 20$ MeV, has a large influenceon analytic properties of the QCD grand-canonical thermodynamic potential. Aclassical van der Waals equation is used to determine these unexpected featuresdue to dense cold matter qualitatively. The existence of the nuclear mattercritical point results in thermodynamic branch points, which are located atcomplex chemical potential values, for $T > T_c \simeq 20$ MeV, and exhibit amoderate model dependence up to rather large temperatures $T \lesssim 100$ MeV.The behavior at higher temperatures is studied using the van der Waals hadronresonance gas (vdW-HRG) model. The baryon-baryon interactions have a decisiveinfluence on the QCD thermodynamics close to $\mu_B = 0$. In particular,nuclear matter singularities limit the radius of convergence $r_{\mu_B/T}$ ofthe Taylor expansion in $\mu_B/T$, with $r_{\mu_B/T} \sim 2-3$ values at $T\sim 140-170$ MeV obtained in the vdW-HRG model.

Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD