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In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average equals the time average. [1] In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime.
Glasses present a challenge to the ergodic hypothesis; time scales are assumed to be in the millions of years, but results are contentious. Spin glasses present particular difficulties. Formal mathematical proofs of ergodicity in statistical physics are hard to come by; most high-dimensional many-body systems are assumed to be ergodic, without ...
Ergodic theory is often concerned with ergodic transformations.The intuition behind such transformations, which act on a given set, is that they do a thorough job "stirring" the elements of that set. E.g. if the set is a quantity of hot oatmeal in a bowl, and if a spoonful of syrup is dropped into the bowl, then iterations of the inverse of an ergodic transformation of the oatmeal will not ...
In probability theory, a stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity.In essence this implies that the random process will not change its statistical properties with time and that its statistical properties (such as the theoretical mean and variance of the process) can be deduced from a single, sufficiently long sample (realization) of the ...
Shivering — shaking of the body in response to early hypothermia in warm-blooded animals. Sneeze or sternutation — a convulsive expulsion of air from the lungs normally triggered by irritation of the nasal mucosa in the nose. Startle-evoked movement — involuntary initiation of a planned movement in response to a startling stimulus ...
In physics and thermodynamics, the ergodic hypothesis [1] says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time.
So-called "trivial" examples are usually the most suitable to illustrate delicate concepts, as when well-chosen they allow to grasp the important part of the theory at once, and the flat torus gives a good idea about ergodicity of geodesic flows even if it is much less rich than the general case.
Electrophysiology (from Greek ἥλεκτ, ēlektron, "amber" [see the etymology of "electron"]; φύσις, physis, "nature, origin"; and -λογία, -logia) is the branch of physiology that studies the electrical properties of biological cells and tissues.