BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

ERGODICITY 1)2)

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Character of a system in which the average values of the variables evolve through time within the set of their statistically invariant values over all possible configurations.

Ergodicity reflects the existence of subjacent global and invariant conditions which determine the behavior of the variables only in a statistical way, but within limits.

Y. SINAI considers as the basic problem of ergodic theory: "the analysis of the causes generating the appearance of statistical laws in dynamic systems" (1992, p.69).

The behavior of an ergodic system evolves within a phases space that becomes divided into subspaces. As expressed by S. DINER: "Ergodic theory is basically a theory of the sets of trajectories" (1992, p.348).

As shown by BIRKHOFF (1931), the most significant characteristic of ergodicity is that the average behavior of the system over a sufficient lapse of time tends to be equal to the average configurations in space. This average on space is independent of the trajectory considered and the average in time is independent of the initial point. The behavior is thus not truly random and could be called para-random.

In consequence, the behavior of chaotic systems, with a number of initial conditions, tends to be ergodic.

→ Ergodic relation, (according to ASHBY).

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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