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

Sergio Curilef; Constantino Tsallis

doi:10.1016/S0375-9601(99)00727-6

paper

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

arXiv:cond-mat/9911152 · doi:10.1016/S0375-9601(99)00727-6

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

7 pages and 6 PS-figures, RevTeX, to appear in Physics Letters A

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

Abstract

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