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 = -∑i=1Wpi lnpi 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=1W piqe/qe - 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.