Statistical characterization of the standard map
Makaleler > Tam Makale · 2017
Yazarlar: Guiomar Ruiz, Ugur Tirnakli, Ernesto P Borges, Constantino Tsallis
Journal of Statistical Mechanics: Theory and Experiment, Uluslararası, Wos, 2017, cilt 2017, ss 063403-063403
Özet
Abstract The standard map, paradigmatic conservative system in the ( x , p ) phase space, has been recently shown (Tirnakli and Borges (2016 Sci. Rep . 6 23644)) to exhibit interesting statistical behaviors directly related to the value of the standard map external parameter K . A comprehensive statistical numerical description is achieved in the present paper. More precisely, for large values of K (e.g. K = 10) where the Lyapunov exponents are neatly positive over virtually the entire phase space consistently with Boltzmann–Gibbs (BG) statistics, we verify that the q -generalized indices related to the entropy production q e n t , the sensitivity to initial conditions q s e n , the distribution of a time-averaged (over successive iterations) phase-space coordinate q s t a t , and the relaxation to the equilibrium final state q r e l , collapse onto a fixed point, i.e. q e n t = q s e n = q s t a t = q r e l = 1 . In remarkable contrast, for small values of K (e.g. K = 0.2) where the Lyapunov exponents are virtually zero over the entire phase space, we verify q e n t = q s e n = 0 ,