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Ergodicity

In mathematics, especially in ergodic theory, ergodicity is a way of saying that a dynamical system behaves as one indivisible statistical system, rather than being composed of statistically distinguishable subsystems. More precisely, a measure-preserving dynamical system is ergodic if every invariant measurable set has either measure zero or full…

History, Ergodicity in physics and geometry & Informal explanation and motivation

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Overview

Informal explanation and motivation

History and etymology

Ergodicity in physics and geometry

Definition for discrete-time systems

Definition for continuous-time dynamical systems

Ergodicity in compact metric spaces

Probabilistic interpretation: ergodic processes

Generalisations

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Map overview Semantic statistics

Ergodicity

Nodes92
Edges91
Triples39
Avg. degree1.98
Density0.021739
Components1

How this topic connects Entity context

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Ergodicity

Top relations

related to Simple dynamical systems · 7
Ergodicity → Arnold's, Basic, Bernoulli, Irrational, Lebesgue, Other, These
related to In statistical mechanics · 6
Ergodicity → For, Hamiltonian, Important, In, Rigorous, This
related to Measurable sets and invariant events · 6
Ergodicity → Borel, Both, For, In, The, When
related to Physical motivation · 4
Ergodicity → For, Hamiltonian, In, The
related to Generalisations · 3
Ergodicity → If, Let, The
related to In quantum mechanics · 3
Ergodicity → In, Related, These
related to Representation-theoretic formulation · 3
Ergodicity → Hilbert, In, Let
is a · 2
Ergodicity → minimal dynamical system, way of saying that a dynamical system behaves as one indivisible statistical system
related to Ergodicity in physics and geometry · 2
Ergodicity → In, The
related to Definition for discrete-time systems · 1
Ergodicity → Ergodic

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Important terminology

ergodic displaystyle measure invariant mu space probability measurable system every mathbb measures mixing sets mathcal example set time orbit left

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ergodicityis away of saying that a dynamical system behaves as one indivisible statistical system0.90text
Ergodicityis aminimal dynamical system0.90text
lim Tinstance ofthis asks whether a time average0.80text
Ergodicityrelated to Definition for discrete-time systemsErgodic0.60section
Ergodicityrelated to Ergodicity in physics and geometryIn0.60section
Ergodicityrelated to Ergodicity in physics and geometryThe0.60section
Ergodicityrelated to GeneralisationsThe0.60section
Ergodicityrelated to GeneralisationsLet0.60section
Ergodicityrelated to GeneralisationsIf0.60section
Ergodicityrelated to In quantum mechanicsIn0.60section
Ergodicityrelated to In quantum mechanicsRelated0.60section
Ergodicityrelated to In quantum mechanicsThese0.60section

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