Nonextensive Statistical Mechanics

7.10 Other Sciences 297Fig. 7.105 Frequency-rank distributions for corpus of Shakespeare and Dickens. The solid linesare fittings using Eq. (6.2) (from [791]).ab=1.0510 –2 =310 –410 –5f(s)10 –610 –810 –710 –910 –1 Bestfit parametersr=1.3210 –3p n(n)(R=0.998)0.86 ± 0.0050.0022 ±0.00005q 1.95 ± 0.01r 1.32 ± 0.01q=1.9510 –102606 books in English (N=183403300, V=448359)10 –112606 books in English (N=183403300, V=448359)10 –1210 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7s10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7nFig. 7.106 Data from a corpus of 2606 books in English: frequency-rank distribution (left), andprobability density function (right). The solid lines are fittings using crossover statistics: see detailsin [791].exhibit connections with nonextensive statistics. Illustrative results are shownin Figs. 7.107, 7.108, 7.109, and 7.110.ii. TransportationThe train delays of the British railway network have been relatively well fittedby q-exponential forms [279]: see Fig. 7.111.iii. Social sciencesMany social phenomena have been addressed on grounds related to q-statistics,such as urban agglomerations [797], circulation of magazines and newspapers[798], football dynamics [800], among others. Some typical results areshown in Figs. 7.112 and 7.113. In the context of other sciences as well, suchas musicology [281] and cognitive sciences [792–795], nonextensive conceptshave been evoked.