Figure 3

(a–c) Exact Rényi entropy S _α (blue dots) and its asymptotic approximation (27) (continuous red line) for α = 1/2, 3/5, 3/4, 1, 3/2, 2, 3 (top to bottom) in (a) a symmetric configuration with r = 3, s = 2, γ _x  = 1/2, γ _p  = 1/3, (b) an asymmetric configuration with r = 7, s = 4, γ _x  = 1/2, γ _p  = 1/4 (cf. Fig. 4), and (c) a symmetric configuration with r = 10, s = 5, γ _x  = 1/2, γ _p  = 1/4. (d–f) Difference ε between the exact entropy S _α and its approximation (27) for the above configurations and (d) α = 1/2, (e) α = 1 (von Neumann entropy), and (f) α = 2. The red lines represent the corresponding curves f(N)N ^{−min(2,2/α)}, with \(f(N)={\sum }_{k=0}^{{k}_{\max }}{a}_{k}\,\cos (k\nu N)\) given in Table 1.