On the upper bound of entropy production rate from particle multiplicity in heavy ion collisions

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