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. Ln 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 less than or equal to alpha less than or equal to D). Particular attention is paid 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 --> infinity limit (N = number of molecules), finite for alpha > D and diverge for alpha less than or equal to D (as (alpha - D)(-1) for alpha/D --> 1 + 0). However, the variables T-c* = T-c/N* and P-c* = P-c/N* with N* = [ N1-alpha/D - 1]/[1 - alpha/D] remain 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. (C) 1999 Elsevier Science B.V. All rights reserved.