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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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Why doesn't the ergodic hypothesis hold for most systems?

Symmetry breaking in general breaks ergodicity. Take, for example, a magnet. … Since statistical mechanics also aims to (and does) explain the behavior of these types of materials as well, it shouldn't need to depend on ergodicity to do so. …
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