Definitions for ergodicity
-gəˈdɪs ɪ tier·god·ic·i·ty

Princeton's WordNetRate this definition:0.0 / 0 votes

1. ergodicitynoun

   an attribute of stochastic systems; generally, a system that tends in probability to a limiting form that is independent of the initial conditions

WiktionaryRate this definition:0.0 / 0 votes

1. ergodicitynoun

   The condition of being ergodic

2. ergodicitynoun

   The extent to which something is ergodic

WikipediaRate this definition:0.0 / 0 votes

1. Ergodicity

   In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point. Equivalently, a sufficiently large collection of random samples from a process can represent the average statistical properties of the entire process. Ergodicity is a property of the system; it is a statement that the system cannot be reduced or factored into smaller components. Ergodic theory is the study of systems possessing ergodicity. Ergodic systems occur in a broad range of systems in physics and in geometry. This can be roughly understood to be due to a common phenomenon: the motion of particles, that is, geodesics on a hyperbolic manifold are divergent; when that manifold is compact, that is, of finite size, those orbits return to the same general area, eventually filling the entire space. Ergodic systems capture the common-sense, every-day notions of randomness, such that smoke might come to fill all of a smoke-filled room, or that a block of metal might eventually come to have the same temperature throughout, or that flips of a fair coin may come up heads and tails half the time. A stronger concept than ergodicity is that of mixing, which aims to mathematically describe the common-sense notions of mixing, such as mixing drinks or mixing cooking ingredients. The proper mathematical formulation of ergodicity is founded on the formal definitions of measure theory and dynamical systems, and rather specifically on the notion of a measure-preserving dynamical system. The origins of ergodicity lie in statistical physics, where Ludwig Boltzmann formulated the ergodic hypothesis.

ChatGPTRate this definition:0.0 / 0 votes

1. ergodicity

   Ergodicity is a property of dynamic systems, particularly in thermodynamics and statistics, that essentially means all accessible states or situations of a system will be eventually and repeatedly visited if you wait for a long enough time. It is the concept that, over a long period of time, a system will explore and encompass all possible states. This property is often used in the context of time averages and is an assumption that underlies many models in economics, physics and other fields.

WikidataRate this definition:0.0 / 0 votes

1. Ergodicity

   In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states. In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics. In statistics, the term describes a random process for which the time average of one sequence of events is the same as the ensemble average.

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1. • Randomness

How to pronounce ergodicity?

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How to say ergodicity in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of ergodicity in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of ergodicity in Pythagorean Numerology is: 7

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=ergodicity
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Ergodicity
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Ergodicity
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=ergodicity