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The hypothesis that the relevant long-time behavior samples the invariant energy surface sufficiently for time averages to agree with ensemble averages. Strict mathematical ergodicity is neither established for all physical systems nor required for every successful equilibrium calculation.
wp-physics-ergodic-hypothesiswp-math-ergodic-theorymit-ocw-ergodic-theorytong-statistical-physicsEach relation below ends at this concept.
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Measure-theoretic ergodicity supplies the precise invariant-set condition invoked by the physical ergodic hypothesis; actual equilibrium statistical mechanics does not require every microscopic system to be strictly ergodic.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-math-ergodic-theorywp-physics-ergodic-hypothesismit-ocw-ergodic-theorytong-statistical-physicsEach relation below starts at this concept.
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The ergodic hypothesis supplies one route from long-time microscopic averages to invariant ensemble averages, but modern equilibrium statistical mechanics does not require strict ergodicity of every model.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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