That this was so became known as the ergodic hypothesis.    From Wordnik.com.  [Philosophy of Statistical Mechanics] Reference

If the process is nonstationary, it is not ergodic.    From Wordnik.com.  [Paul Linsay's Poisson Fit « Climate Audit] Reference

And you have just created a text in an ergodic manner.    From Wordnik.com.  [thinking with my fingers] Reference

True… but if they are ergodic, you can interchange them.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

The ergodic hypothesis is often assumed in statistical analysis.    From Wordnik.com.  [Paul Linsay's Poisson Fit « Climate Audit] Reference

Plato, J. von (1992), "Boltzmann's ergodic hypothesis", Arch. Hist.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

Blatt, J. M (1959), "An alternative approach to the ergodic problem".    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

And perhaps ergodic narratives inherently resist the linearity of conclusion.    From Wordnik.com.  [Rubicite Breastplates & Narrative Nudges] Reference

From a mathematical point of view, flows in general are not proven to ergodic.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

The mathematical discipline of ergodic theory developed out of these early ideas.    From Wordnik.com.  [Philosophy of Statistical Mechanics] Reference

But what makes you think that the consequences of the shorter timescales are ergodic?.    From Wordnik.com.  [Unthreaded #18 « Climate Audit] Reference

If, in addition, msubr=µ for almost all realisations the process is said to be ergodic.    From Wordnik.com.  [More Bender on Hurricane Counts « Climate Audit] Reference

In essence, they suggest that Boltzmann somehow silently relied on the ergodic hypothesis.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

And when he did return to the ergodic hypothesis in (1871b), it was with much more caution.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

The Ehrenfests have suggested that the ergodic hypothesis played a much more fundamental role.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

Lectures on Gas Theory (1896,1898), for example, does not even mention the ergodic hypothesis.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

In a non-ergodic system nonlinear dynamics, exponential growth, this presents a major problem.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

It is my understanding that not only are the planetary orbits chaotic, they are non-ergodic too.    From Wordnik.com.  [Initial value vs. boundary value problems | Serendipity] Reference

One approach to deriving the kinetic equations relies upon work which generalizes ergodic theory.    From Wordnik.com.  [Philosophy of Statistical Mechanics] Reference

At best, you can say “have not been proven to be ergodic either using mathematics or empirically”.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

If the two have the same statistical properties, they are interchangeable, and the process is ergodic.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

Yet the Ehrenfests simultaneously expressed strong doubts about the validity of the ergodic hypothesis.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

Particularly notorious are the role of the ergodic hypothesis and the status of the so-called H-theorem.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

Games contain ergodic texts, just as they can contain or communicate little stories, videos or pictures.    From Wordnik.com.  [thinking with my fingers] Reference

I like to run regressions and believe the world is basically ergodic and I don't think they would have me.    From Wordnik.com.  [What's in a Name?] Reference

The permutational argument is only discussed as an aside, and the ergodic hypothesis is not mentioned at all.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

They are ergodic texts yes, I know Espen Aarseth has already concluded this, but they don't stop at being ergodic texts.    From Wordnik.com.  [thinking with my fingers] Reference

Similarly, they pointed out that under the ergodic hypothesis infinite time averages and ensemble averages were identical.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

First, the difference between the approach relying on the ergodic hypothesis and that relying on the SZA is rather striking.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

Maxwell's paper seems to have revived Boltzmann's interest in the ergodic hypothesis, which he had been avoiding for a decade.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

There is a major confusion among modern commentators about the role and status of the ergodic hypothesis in Boltzmann's thinking.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

There are a very few situations in which solutions are not ergodic, but as an empirical matter, it takes some doing to find them.    From Wordnik.com.  [Exponential Growth in Physical Systems #2 « Climate Audit] Reference

One might then still conjecture that if the system is quasi-ergodic, the only continuous stationary distribution is microcanonical.    From Wordnik.com.  [Boltzmann's Work in Statistical Physics] Reference

At the end of his manifesto, I started wondering if what he was describing is games at all, or something else: ergodic persuasion, perhaps?.    From Wordnik.com.  [SGS day two] Reference

A good illustration of this idea comes from ergodic theory.    From Wordnik.com.  [American Scientist Online] Reference

Inconsistency over time is a feature of a non-ergodic world.    From Wordnik.com.  [Jennifer Marohasy] Reference

Classical ergodic theory begins with a dynamical system or stochastic process.    From Wordnik.com.  [American Scientist Online] Reference

An ergodic vignette is not a story in the sense that there are dramatic plot arcs.    From Wordnik.com.  [PopMatters] Reference

Maybe Emanuel’s Atlantic basin subsystem is not far from ergodic?.    From Wordnik.com.  [New Emanuel Presentation « Climate Audit] Reference