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Entropy evolution at generic power-law edge of chaos

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=−∑=1pi*lnpi equals the sum of the positive Lyapunov exponents)._x000D_

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−∑=1−1(1=) with ≤1._x000D_

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._x000D_

C. Tsallis, E.P. Borges, A.R. Plastino, Entropy evolution at generic power-law edge of chaos, Chaos, Solitons & Fractals 174 (2023) 113855.

Constantino Tsallis, External Faculty at the Complexity Science Hub, celebrates his 80th birthday

Constantino Tsallis

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