Generalized dynamical entropies in weakly chaotic systems

Abstract

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may define a generalized, Tsallis type dynamical entropy that increases linearly with time. It characterizes a maximal gain of information about the system that increases as a power of time. However, this entropy cannot be chosen independently from the choice of coarse graining lengths and it assigns positive dynamical entropies also to fully integrable systems. By considering these dependencies in detail one usually will be able to distinguish weakly chaotic from fully integrable systems.

Submitted to Physica D for the proceedings of the Santa Fe workshop of November 6-9, 2002 on Anomalous Distributions, Nonlinear Dynamics and Nonextensivity. 8 pages and two figures

References in corpus (3)

• Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas
• Finite thermal conductivity in 1D models having zero Lyapunov exponents
• Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

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