Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial condi- tions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been shown to coincide with the Pesin identity. Numerical evi- dences support 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.
Entropy production and pesin-like identity at the onset of chaos
TONELLI, ROBERTO;MEZZORANI, GIUSEPPE;
2006-01-01
Abstract
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial condi- tions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been shown to coincide with the Pesin identity. Numerical evi- dences support 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.
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