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 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 with .
For such weakly chaotic systems, power-law divergences emerge involving a set of microscopic indices ’s and the associated generalized Lyapunov coefficients. We establish the connection between these quantities and , where Kqe is the Sqe entropy production rate.
C. Tsallis, E.P. Borges, A.R. Plastino, Entropy evolution at generic power-law edge of chaos, Chaos, Solitons & Fractals 174 (2023) 113855.