We review the evolution of some statistical and thermodynamical quantities measured in difference sizes of high-energy collisions at different energies. We differentiate between intensive and extensive quantities and discuss the importance of their d
istinguishability in characterizing possible critical phenomena of nuclear collisions at various energies with different initial conditions.
Finding out universal conditions describing the freeze-out parameters was a subject of various phenomenological studies. In the present work, we introduce a new condition based on constant trace anomaly (or interaction measure) calculated in the hadr
on resonance gas (HRG) model. Various extensions to the {it ideal} HRG which are conjectured to take into consideration different types of interactions have been analysed. When comparing HRG thermodynamics to that of lattice quantum chromodynamics, we conclude that the hard-core radii are practically irrelevant, especially when HRG includes all resonances with masses less than $2~$GeV. It is found that the constant trace anomaly (or interaction measure) agrees well with most of previous conditions.
