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Entropy evolution at generic power-law edge of chaos

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  • Tsallis, Constantino
  • Borges, Ernesto P.
  • Plastino, Angel R.

Abstract

For strongly chaotic classical systems, a basic statistical–mechanical connection is provided by the averaged Pesin-like identity (the production rate of the Boltzmann–Gibbs entropy SBG=−∑i=1Wpilnpi equals the sum of the positive Lyapunov exponents). In contrast, at a generic edge of chaos (vanishing maximal Lyapunov exponent) we have a subexponential divergence with time of initially close orbits. This typically occurs in complex natural, artificial and social systems and, for a wide class of them, the appropriate entropy is the nonadditive one Sqe=1−∑i=1Wpiqeqe−1(S1=SBG) with qe≤1. For such weakly chaotic systems, power-law divergences emerge involving a set of microscopic indices {qk}’s and the associated generalized Lyapunov coefficients. We establish the connection between these quantities and (qe,Kqe), where Kqe is the Sqe entropy production rate.

Suggested Citation

  • Tsallis, Constantino & Borges, Ernesto P. & Plastino, Angel R., 2023. "Entropy evolution at generic power-law edge of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007567
    DOI: 10.1016/j.chaos.2023.113855
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    References listed on IDEAS

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    1. R. Hanel & S. Thurner & C. Tsallis, 2009. "Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 263-268, November.
    2. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Adib, Artur B. & Moreira, André A. & Andrade Jr, José S. & Almeida, Murilo P., 2003. "Tsallis thermostatistics for finite systems: a Hamiltonian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 276-284.
    4. Biró, T.S., 2013. "Ideal gas provides q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3132-3139.
    5. Almeida, M.P., 2001. "Generalized entropies from first principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 424-432.
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    Cited by:

    1. Sabe, Naval R. & Pakhare, Sumit S. & Gade, Prashant M., 2024. "Synchronization transitions in coupled q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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