Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps (Q5954870)

The relationship between the Boltzmann equilibrium thermodynamic entropy and the Kolmogorov-Sinai entropy is illustrated through several numerical examples for conservative and dissipative chaotic maps. At the chaos treshold, where the sensitivity to initial conditions is not exponential, but power-law like, the nonextensive entropic form introduced by Tsallis is adopted. A linear growth for the generalized entropy is obtained for the value of the exponent of the power-law that is different from 1 (for which the standard entropy is recovered). This entropic index appears to be characteristic of the dynamical system.