Kolmogorov–Sinai entropy

E695939

dynamical systems invariant entropy mathematical concept

Kolmogorov–Sinai entropy is a fundamental invariant in dynamical systems theory that quantifies the average rate of information production or unpredictability of a measure-preserving transformation.

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Statements (47)

Predicate	Object
instanceOf	dynamical systems invariant ⓘ entropy ⓘ mathematical concept ⓘ
alsoKnownAs	KS entropy NERFINISHED ⓘ metric entropy NERFINISHED ⓘ
appliesTo	measure-preserving dynamical system ⓘ measure-preserving transformation ⓘ
characterizes	randomness of trajectories ⓘ
comparedWith	topological entropy via variational principle ⓘ
definedAs	supremum of entropies over all finite measurable partitions ⓘ
definedFor	probability space with measure-preserving transformation ⓘ
definedUsing	Shannon entropy of partitions ⓘ measurable partitions ⓘ
describes	average rate of information production ⓘ unpredictability of a dynamical system ⓘ
field	dynamical systems theory ⓘ ergodic theory ⓘ information theory ⓘ
hasImplication	positive value implies chaotic behavior in many systems ⓘ
hasRole	fundamental invariant in dynamical systems theory ⓘ
hasUnit	bits per unit time ⓘ nats per unit time ⓘ
introducedIn	1950s ⓘ
isInvariantOf	measure-preserving transformation ⓘ
mathematicalDomain	ergodic theory ⓘ measure theory ⓘ probability theory ⓘ
namedAfter	Andrey Kolmogorov NERFINISHED ⓘ Ya. G. Sinai NERFINISHED ⓘ
property	can be infinite ⓘ is invariant under measure-preserving isomorphisms ⓘ is nonnegative ⓘ
quantifies	complexity of orbits ⓘ rate of information loss about initial conditions ⓘ
relatedTo	Bernoulli shifts NERFINISHED ⓘ Lyapunov exponent NERFINISHED ⓘ Pesin theory NERFINISHED ⓘ Shannon entropy NERFINISHED ⓘ measure-theoretic entropy ⓘ symbolic dynamics ⓘ topological entropy ⓘ
satisfies	Kolmogorov–Sinai theorem NERFINISHED ⓘ
specialCaseOf	measure-theoretic entropy ⓘ
usedIn	information-theoretic analysis of dynamical systems ⓘ statistical mechanics ⓘ
usedToClassify	measure-preserving dynamical systems up to isomorphism ⓘ
usedToDetect	chaos in dynamical systems ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Lyapunov exponents → relatedTo → Kolmogorov–Sinai entropy ⓘ

Lectures on Ergodic Theory → subject → Kolmogorov–Sinai entropy ⓘ

Yakov Sinai → notableWork → Kolmogorov–Sinai entropy ⓘ

Yakov Sinai → notableConcept → Kolmogorov–Sinai entropy ⓘ