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Here we develop an original approach to investigate the grand canonicalpartition function of the multicomponent mixtures of Boltzmann particles withhard-core interaction in finite and even small systems of the volumes above 20fm$^3$. The derived expressions of the induced surface tension equation ofstate are analyzed in details. It is shown that the metastable states, whichcan emerge in the finite systems with realistic interaction, appear at veryhigh pressures at which the hadron resonance gas, most probably, is notapplicable at all. It is shown how and under what conditions the obtainedresults for finite systems can be generalized to include into a formalism theequation for curvature tension. The applicability range of the obtainedequations of induced surface and curvature tensions for finite systems isdiscussed and their close relations to the equations of the morphologicalthermodynamics are established. The hadron resonance gas model on the basis ofthe obtained advanced equation of state is worked out. Also, this model isapplied to analyze the chemical freeze-out of hadrons and light nuclei with thenumber of (anti-)baryons not exceeding 4, including the most problematic ratiosof hyper-triton and its antiparticle. Their multiplicities were measured by theALICE Collaboration in the central lead-lead collisions at the center-of-massenergy $\sqrt{s_{\rm NN}} =$ 2.76 TeV.

Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics