Europhys. Lett.
Volume 62, Number 6, June 2003
Page(s) 808 - 814
Section General
Published online 01 June 2003
DOI: 10.1209/epl/i2003-00444-0
Europhys. Lett., 62 (6) , pp. 808-814 (2003)

Universal relaxation in nonextensive systems

F. Brouers1, 2 and O. Sotolongo-Costa2

1  Department of Physics, Liège University - Liège, Belgium
2  Henri Poincaré Chair of Complex Systems, Havana University - Havana, Cuba

(Received 7 June 2002; accepted in final form 30 April 2003)

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter $\alpha$ and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived from an extension of the Lévy central-limit theorem. They are in full agreement with the Jonscher universality principle. Moreover, our model gives a physical interpretation of the mathematical parameters of the Weron stochastic theory and opens new paths to understand the ubiquity of self-similarity and power laws in the relaxation of large classes of materials in terms of their fractal and nonextensive properties.

05.70.-a - Thermodynamics.
05.90.+m - Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems.
05.45.Df - Fractals.

© EDP Sciences 2003