The Contribution of A.N. Kolmogorov to the Notion of Entropy View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1988

AUTHORS

Mario Casartelli

ABSTRACT

The immediate source of the concept of entropy of a dynamical system, introduced by A. N. Kolmogorov in 1958, was a definite and typical problem in the context of abstract dynamical systems, the problem of isomorphism. In spite of being so natural, it is far from being immediately evident or soluble. Consider, for instance, a classical case of probabilistic games (mathematically: Bernoulli Shifts): it is quite obvious that, in a repeated experiment, tossing a coin is equivalent to tossing a die and considering the outcomes only in terms of whether they are odd or even; should it also be equivalent to tossing a die and conceiving of the outcomes as ranging from 1 to 6? It was by using his new ‘metric invariant’ — the dynamical or K-entropy — that Kolmogorov succeeded in giving a negative answer to this old and only apparently simple problem. More... »

PAGES

149-159

References to SciGraph publications

Book

TITLE

Probability in the Sciences

ISBN

978-94-010-7877-1
978-94-009-3061-2

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-009-3061-2_10

DOI

http://dx.doi.org/10.1007/978-94-009-3061-2_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1007418544


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