Definitions for ergodic
ɜrˈgɒd ɪker·god·ic

Princeton's WordNetRate this definition:1.0 / 1 vote

1. ergodicadjective

   positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions

WiktionaryRate this definition:0.0 / 0 votes

1. ergodicadjective

   Of or relating to certain systems that, given enough time, will eventually return to previously experienced state.

2. ergodicadjective

   Of or relating to a process in which every sequence or sample of sufficient size is equally representative of the whole.

3. Etymology: International Scientific Vocabulary (+ -ic)

WikipediaRate this definition:0.0 / 0 votes

1. ergodic

   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. ergodic

   Ergodic is a term used mainly in physics and mathematics, particularly in statistics, dynamical systems theory and information theory, to describe a system or process in which every possible state or output is equally likely to occur over a long period of time. It also refers to the property of a system where the average over time (time average) and the average over the space of all states (ensemble average) are the same. Essentially, an ergodic system thoroughly explores all accessible states.

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1. • Statistics

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Numerology

1. Chaldean Numerology

   The numerical value of ergodic in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of ergodic in Pythagorean Numerology is: 7

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=ergodic
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Ergodic
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Ergodic
4. ^ ChatGPT
   https://chat.openai.com