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−α. Thermodynamic extensivity (nonextensivity) is observed for α > D (0 ≤ α ≤ D). Particular attention is payed to the liquid-gas critical point located, in the temperature-pressure plane, at (Tc, Pc). (Tc, Pc) are, in the N → ∞ limit (N ≡ number of molecules), finite for α > D and diverge for α ≤ D (as (α − D) for α/D → 1 + 0). However, the variables T ∗ c ≡ Tc/N ∗ and P ∗ c ≡ Pc/N ∗ with N∗ ≡ [N1−α/D − 1]/[1 − α/D] remain 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.