  We provide a simple derivation for particle production in heavy-ion
collisions that is proportional to the rate of entropy production. We find that
the particle production depends only on the power of the centre-of-mass
collision energy $\sqrt{s_{\rm NN}}$ and the effective phase-space/volume (e.g.
geometry of the collision approximated by the number of nucleons participating
in the collision $N_{\rm part}$). We show that at low-energies the
pseudo-rapidity density of particles per participating nucleon pair scales
linearly with $\sqrt{s_{\rm NN}}$ while at high-energies with $\sqrt{s_{\rm
NN}}^{1/3}$. The $\sqrt{s_{\rm NN}}^{1/3}$ region is directly related to
sub-nucleon degrees of freedom and creation of a quark-gluon plasma (QGP). This
picture explains experimental observation that the shape of the distributions
of pseudorapidity-density per nucleon pair of charged particles does not depend
on $\sqrt{s_{\rm NN}}$ over a large span of collision energies. We provide an
explanation of the scaling and connect it with the maximum rate per unit time
of entropy production. We conclude with remarks on the hadron-parton phase
transition. In particular, our considerations suggest that the pseudo-rapitidy
density of the produced particles per $N_{\rm part}/2$ larger than
approximately 1 (excluding particles from jet fragmentation) is a signature of
a QGP formation.
