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