NOISE, CHAOS, AND (EPSILON, TAU)-ENTROPY PER UNIT TIME

被引:173
作者
GASPARD, P
WANG, XJ
机构
[1] UNIV LIBRE BRUXELLES,CTR NONLINEAR PHENOMENA & COMPLEX SYST,B-1050 BRUSSELS,BELGIUM
[2] UNIV CHICAGO,JAMES FRANCK INST,CHICAGO,IL 60637
来源
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS | 1993年 / 235卷 / 06期
关键词
D O I
10.1016/0370-1573(93)90012-3
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The degree of dynamical randomness of different time processes is characterized in terms of the (epsilon, tau)-entropy per unit time. The (epsilon, tau)-entropy is the amount of information generated per unit time, at different scales tau of time and epsilon of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (epsilon, tau)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice ps automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (epsilon, tau)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.
引用
收藏
页码:291 / 343
页数:53
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