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The rate of entropy increase at the edge of chaos | | V. Latora
; M. Baranger
; A. Rapisarda
; C. Tsallis
; | | Date: |
27 Jul 1999 | | Journal: | Phys.Lett. A273 (2000) 97 | | Subject: | Statistical Mechanics; Cellular Automata and Lattice Gases; Chaotic Dynamics | cond-mat.stat-mech astro-ph chao-dyn comp-gas hep-th nlin.CD nlin.CG nucl-th | | Abstract: | Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This connection is here generalized to a simple dissipative system, the logistic map, and especially to the chaos threshold of the latter, the edge of chaos. It is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon entropy is not appropriate. Instead, the non-extensive entropy $S_qequiv frac{1-sum_{i=1}^W p_i^q}{q-1}$, must be used. The latter contains a parameter q, the entropic index which must be given a special value $q^*
e 1$ (for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos under consideration. The same q^* enters also in the description of the sensitivity to initial conditions, as well as in that of the multifractal spectrum of the attractor. | | Source: | arXiv, cond-mat/9907412 | | Services: | Forum | Review | PDF | Favorites | |
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