this distribution.

In Figure 7 we plot the ratio of entropy to total baryon number $S/B$ for the hadronic and quark–gluon plasma phase for fixed beam energies. Fixed beam energy means that initially both the energy density and the baryon number density of the system is given which then determine the corresponding entropies via the equation of state. We use the equation of state discussed in [@us] for all further calculations. It is helpful to consider two extreme and opposite scenarios. Either the matter stays all the time in the hadronic phase, or the matter has been completely converted to quark–gluon plasma by the time $t_0$ and only hadronizes later. The difference of the entropies produced in these two scenarios is given by the difference of the two curves in Figure 7. It represents an upper limit on the additional number of pions produced. Since the temperature is comparable to or larger than the pion mass the excess entropy is proportional to the maximum number of excess pions $$\begin{aligned}
3 \frac{\Delta N_{\rm -}}{B} = \frac{1}{3.6} \frac{\Delta S}{B}\, .
\label{npi}\end{aligned}$$ The number of additional negatively charged pions per baryon $\Delta N_{\rm -}/B$ is linearly related to the entropy difference $\Delta S$ 