  Experimental data on inclusive cross sections of particles produced in high
energy proton-(anti)proton collisions at ISR, RHIC, and Tevatron are analyzed
in the framework of $z$-scaling. New features of the scaling function $\psi(z)$
are established. These are flavor independence of $\psi(z)$ including particles
with heavy flavor content and saturation at low $z$. The flavor independence
means that the shape of the scaling function $\psi(z)$ is the same for
different hadron species. The saturation corresponds to flattening of $\psi(z)$
for $z<0.1$. Relations of model parameters used in data $z$-presentation with
some thermodynamical quantities (entropy, specific heat, temperature) are
discussed. It is shown that behavior of the particle spectra at low $z$ is
controlled by a parameter $c$ interpreted as a specific heat of the created
medium associated with production of the inclusive particle. The saturation
regime of $\psi(z)$ observed at low $z$ is assumed to be preferable in
searching for phase transitions of hadron matter and for study of
non-perturbative QCD in high energy proton-(anti)proton collisions at U70,
RHIC, Tevatron, and LHC.
