Sporadic randomness: The transition from the stationary to the nonstationary condition

被引:35
作者
Ignaccolo, M
Grigolini, P
Rosa, A
机构
[1] Univ N Texas, Ctr Nonlinear Sci, Denton, TX 76203 USA
[2] CNR, Ist Biofis, Area Ric Pisa, I-56010 Pisa, Italy
[3] Univ Pisa, Dipartimento Fis, I-56127 Pisa, Italy
[4] INFM, I-56127 Pisa, Italy
[5] SISSA, I-34014 Trieste, Italy
来源
PHYSICAL REVIEW E | 2001年 / 64卷 / 02期
关键词
D O I
10.1103/PhysRevE.64.026210
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We address the study of sporadic randomness by means of the Manneville map. We point out that the Manneville map is the generator of fluctuations yielding the Levy processes, and that these processes are currently regarded by some authors as statistical manifestations of a nonextensive form of thermodynamics. For this reason we study the sensitivity to initial conditions with the help of a nonextensive form of the Lyapunov coefficient. The purpose of this research is twofold. The former is to assess whether a finite diffusion coefficient might emerge from the nonextensive approach. This property, at first sight, seems to be plausible in the nonstationary case, where conventional Kolmogorov-Sinai analysis predicts a vanishing Lyapunov coefficient. The latter purpose is to confirm or reject conjectures about the nonextensive nature of Levy processes. We find that the adoption of a nonextensive approach does not serve any predictive purpose: It does not even signal a transition from a stationary to a nonstationary regime. These conclusions are reached by means of both numerical and analytical calculations that shed light on why the Levy processes do not imply any need to depart from the adoption of traditional complexity measures.
引用
收藏
页码:11 / 262111
页数:11
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