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Results tagged with ergodicity
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user 50546
A system is said to be ergodic if time averages are, for a sufficient long time, equivalent to phase space averages. This "ergodic hypothesis" is taken by many authors as the foundation of statistical mechanics.
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Physical distinction between mixing and ergodicity
In addition, we have this chain of implications (proved in the reference):
$$\text{mixing}\Rightarrow\text{weak mixing}\Rightarrow\text{ergodicity}$$
In addition, it can be shown that the notions are … As far as I know, the concept of mixing is introduced for convenience: it is often easier to prove the (weak) mixing property than ergodicity directly, and once mixing is proved, ergodicity follows. …
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