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

Abstract

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 $r^{-α}$. Thermodynamic extensivity (nonextensivity) is observed for $α> D$ ($0\leq α\leq D$). 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 ($N\equiv$ number of molecules), {\em finite} for $α> D$ and {\em diverge} for $α\leq D$ (as $(α- D)^{-1}$ for $α/D \to 1 + 0$). However, the variables $T_c^* \equiv T_c/N^*$ and $P_c^* \equiv P_c/N^*$ with $N^* \equiv [N^{1-α/D} -1]/[1-α/D]$ remain {\em finite for all} $α$. Thus, the extensive and nonextensive regions become unified, as recently conjectured. These results should be useful for discussing gravitation and some special fluids