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Prog. Theor. Phys. Vol. 115 No. 1 (2006) pp. 23-29

[ Full Text PDF : FREE ACCESS (197K) ]

Entropy Production and Pesin-Like Identity at the Onset of Chaos

Roberto Tonelli,1,2,3,* Giuseppe Mezzorani,1,3,** Franco Meloni,1,2,*** Marcello Lissia1,3,**** and Massimo Coraddu1,3,*****

1Dipart. di Fisica dell'Università di Cagliari, I-09042 Monserrato, Italy
2INFO-SLACS Laboratory, I-09042 Monserrato, Italy
3Ist. Naz. Fisica Nucleare (I.N.F.N.) Cagliari, I-09042 Monserrato, Italy

(Received May 23, 2005)

Abstract:

Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two types of behavior are related. Such relationship is analogous to and, under specific conditions, has been shown to coincide with the Pesin identity. Numerical evidence supports the proposal that the statistical formalism can be extended to the edge of chaos by using a specific generalization of the exponential and of the Boltzmann-Gibbs entropy. We extend this picture and a Pesin-like identity to a wide class of deformed entropies and exponentials using the logistic map as a test case. The physical criterion of finite-entropy growth strongly restricts the suitable entropies. The nature and characteristics of this generalization are clarified.


URL : http://ptp.ipap.jp/link?PTP/115/23/
DOI : 10.1143/PTP.115.23


*E-mail: roberto.tonelli@dsf.unica.it
**E-mail: giuseppe.mezzorani@ca.infn.it
***E-mail: franco.meloni@dsf.unica.it
****E-mail: marcello.lissia@ca.infn.it
*****E-mail: massimo.coraddu@ca.infn.it

[ Full Text PDF : FREE ACCESS (197K) ] Citation:

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