Nonextensive Statistical Mechanics

3.1 Playing with Differential Equations – A Metaphor 39e qxq = 2 q = 12.5q = 0q → ∞21.51q = –10.5q → –∞–1.5 –1 –0.5 0 0.5 1 x 1.5Fig. 3.1 The q-exponential function eq x for typical values of q. Forq > 1, it is defined in theinterval (−∞, (q − 1) −1 ); it diverges if x → (q − 1) −1 − 0. For q < 1, it is defined ∀x, andvanishes for all x < −(1 − q) −1 . In the limit x → 0, it is eq x ∼ 1 + x (∀q).1e –x q0.80.60.40.2q = –1q = 0q = 2q = 100 1 2 3 x 4Fig. 3.2 The q-exponential function eq−x for typical values of q: linear–linear scales. For q > 1, itvanishes like [(q − 1)x] −1/(q−1) for x →∞.Forq < 1, it vanishes for x > (1 − q) −1 (cutoff).