Critical Temperature and Nonextensivity in Long-range Interacting Lennard-Jones-like Fluids

Molecular dynamic simulations for systems with $D=2,3$ Lennard-Jones-like interactions are studied. In the model, we assume that, at long distances, the two-body attractive potential decays as $r^{-\alpha }$. Thermodynamic extensivity (nonextensivity) is observed for $\alpha >D$ ($0\leq \alpha \leq D$). Particular attention is payed to the liquid-gas critical point located, in the temperature-pressure plane, at ($T_c,P_c$). ($T_c,P_c$) are, in the $N\to \infty$limit($N\equiv$numberofmolecules),\text{em}finitefor$\alpha > D$and\text{em}divergefor$\alpha \leq D$(as$(\alpha - D)^{-1}$for$\alpha/D \to 1 + 0$)\mathrm{.}However,thevariables$T_c^* \equiv T_c/N^$and$P_c^ \equiv P_c/N^$with$N^ \equiv [N^{1-\alpha/D} -1]/[1-\alpha/D]$ remain {\em finite for all} $\alpha$. Thus, the extensive and nonextensive regions become unified, as recently conjectured. These results should be useful for discussing gravitation and some special fluids