Non-extensive thermodynamics and stationary processes of localization

• Main Authors: Fronzoni, Leone, Grigolini, Paolo, Montangero, Simone
• Format: Journal Article
• Language: English
• Published: 29-07-1999
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.cond-mat/9907458

We focus our attention on dynamical processes characterized by an entropic
index Q<1. According to the probabilistic arguments of Tsallis and Bukman
[C.Tsallis, D.J. Bukman, Phys. Rev. E 54,R2197 (1996)] these processes are
subdiffusional in nature. The non-extensive generalization of the
Kolmogorov-Sinai entropy yielding the same entropic index implies the
stationary condition. We note, on the other hand, that enforcing the stationary
property on subdiffusion has the effect of producing a localization process
occurring within a finite time scale. We thus conclude that the stationary
dynamic processes with Q<1 must undergo a localization process occurring at
finite time. We check the validity of this conclusion by means of a numerical
treatment of the dynamics of the logistic map at the critical point.