Nonextensive Statistical Mechanics

7.10 Other Sciences 295Fig. 7.102 Same model as in Figs. 3 and 4. Left: α-dependance of the values of q and κ for thebest q-exponential fitting of the numerical results for the N = 2 9 network. Right: Thesameforthe values of q for increasingly large networks. In the limits α = 0andα →∞, we recover therandom and neighbor schemes of [51], respectively. The dashed curve corresponds to a possibleheuristic analytical behavior (Figure following [49].).7.8.4 Lennard–Jones ClusterLennard–Jones small clusters (with N up to 14) have been numerically studied [866,867]. The distributions of the number of local minima of the potential energy withk neighboring saddle-points in the configurational phase-space can be quite wellfitted with q-exponentials with q = 2. No explanation is still available for thissuggestive fact. Qualitatively speaking, however, the fact that we are talking of verysmall clusters makes that, despite the fact that the Lennard–Jones interaction is not along-range one thermodynamically speaking (since α/d = 6/3 > 1), all the atomssensibly “see” each other, therefore fulfilling roughly a nonextensive scenario. SeeFig. 7.103. Most probably, a crossover to an extensive scenario might occur forincreasingly large N.7.9 LinguisticsWe briefly present here Zipf’s law and its generalizations. Some of the connectionswhich exist with q-statistics are illustrated in Figs. 7.104, 7.105, and 7.106from [791].7.10 Other Sciencesi. CitationsThe statistical analysis of the citations of scientific papers has become possiblethanks to internet research tools such as those implemented by ISI-Web ofScience and Scopus/Elsevier. Some of these analyses [276, 278, 280, 796, 799]