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).

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.

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.

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