The η /s of the LQCD-EoS complied hadron gas of different sizes approach common minimum near the crossover temperature

We study the temperature dependence of the ratio of the shear viscosity to entropy density for the LQCD-contrasted hadron resonance gas of different finite system-sizes, which may represent the final state hadronic matter, formed in systems of ultra-relativistic collisions. The transport coefficient reaches the lowest common value, for the systems of different sizes of thermalized hadron gas, near the critical temperature $T_{c}$ of the QCD crossover.