The rate of entropy increase at the edge of chaos

@article{Latora1999TheRO,
  title={The rate of entropy increase at the edge of chaos},
  author={Vito Latora and M. Baranger and Andrea Rapisarda and Constantino Tsallis},
  journal={Physics Letters A},
  year={1999},
  volume={273},
  pages={97-103}
}
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… Expand

Figures from this paper

The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
We study the connection between the appearance of a ‘metastable’ behaviour of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy [C. Tsallis, PossibleExpand
The complexity of the logistic map at the chaos threshold
We apply a generalized version of the Kolmogorov–Sinai entropy, based on a non-extensive form, to analyzing the dynamics of the logistic map at the chaotic threshold, the paradigm of power-lawExpand
Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps
Abstract We consider several low-dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative mapsExpand
Generalization of the Kolmogorov–Sinai entropy: logistic-like and generalized cosine maps at the chaos threshold
Abstract We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form S q ≡[1−∑ i =1 W p i q ]/[ q −1] (with S 1 =−∑ i =1 W p i ln p i ) for two families ofExpand
Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos
It is well known that, for chaotic systems, the production of relevant entropy (Boltzmann–Gibbs) is always linear and the system has strong (exponential) sensitivity to initial conditions. In recentExpand
Entropy Production and Pesin-Like Identity at the Onset of Chaos
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 isExpand
Statistical descriptions of nonlinear systems at the onset of chaos
Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of theExpand
Numerical study of the oscillatory convergence to the attractor at the edge of chaos
Abstract.This paper compares three different types of “onset of chaos” in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; theExpand
Information and Helical Mechanism of Entropy Increase
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, weExpand
Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps
AbstractWe introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the (z1, z2)-logarithmic map, corresponds to a generalization ofExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 41 REFERENCES
Estimation of the Kolmogorov entropy from a chaotic signal
While there has been recently a dramatic growth in new mathematical concepts related to chaotic systems, ' the detailed comparison between models and experimental data has lagged somewhat. AfterExpand
A non extensive approach to the entropy of symbolic sequences
Symbolic sequences with long-range correlations are expected to result in a slow regression to a steady state of entropy increase. However, we prove that also in this case a fast transition to aExpand
Circular-like maps: sensitivity to the initial conditions, multifractality and nonextensivity
Dissipative one-dimensional maps may exhibit special points (e.g., chaos threshold) at which the Lyapunov exponent vanishes. Consistently, the sensitivity to the initial conditions has a power-lawExpand
Chaos and statistical mechanics in the Hamiltonian mean field model
Abstract We study the dynamical and statistical behavior of the Hamiltonian mean field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is aExpand
Power-law sensitivity to initial conditions—New entropic representation
Abstract The exponential sensitivity to the initial conditions of chaotic systems (e.g. D = 1) is characterized by the Liapounov exponent λ, which is, for a large class of systems, known to equal theExpand
Kolmogorov-Sinai Entropy Rate versus Physical Entropy
We elucidate the connection between the Kolmogorov-Sinai entropy rate {kappa} and the time evolution of the physical or statistical entropy S . For a large family of chaotic conservative dynamicalExpand
Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed inExpand
Low-dimensional non-linear dynamical systems and generalized entropy
Low dimensional non-linear maps are prototype models to study the emergence of complex behavior in nature. They may exhibit power-law sensitivity to initial conditions at the edge of chaos which canExpand
Dynamical Behaviour at the Onset of Chaos
Power-law divergence of nearby trajectories on the Feigenbaum attractor is discussed in terms of the algebraic index β. A statistical analysis is performed by following a multifractal approach. As aExpand
Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection withExpand
...
1
2
3
4
5
...