the ’exact’ polydisperse BMCSL solution even for moderate polydispersity $s \le 0.3$, which is the maximum value considered in the remaining part of the work. The remaining plots in Figure \[fig3\] display the effect of polydispersity on the PY pressure equation of state as obtained from the energy route and for decreasing values of the temperature $\tau$. In the one component case $s=0$, a van der Waals loop starts to appear when we cross the critical temperature $\tau_c \sim 0.1185$ coming from the high $\tau$ regime. Obviously this signals the onset of a liquid-gas phase transition, and the corresponding phase diagram can be obtained by a standard Maxwell construction by connecting appropriate points with the same pressure. In the presence of polydispersity (here represented by choice IV for size-dependence of the stickiness parameters) the same procedure [*cannot*]{} be applied due to fractionation, as already discussed. Nevertheless, we can clearly see that as $s$ increases, the van der Waals loop region (when present) expands, thus suggesting that phase transition is favored by the presence of polydispersity. A similar feature occurs for the polydisperse van der Waals model [@Bellier-Castella00] and for the numerical results of the PY compressibility equation of state [@Robertus89] 