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The best way to
think about it is to imagine a huge
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ensemble of
systems that all have exactly the same
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energy function.
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The
probability distribution is just the fraction of the
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systems
that are in each possible configuration.
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We could start
with all the systems in the same
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configuration,
or with an equal number of systems in
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each possible
configuration.
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After
running the systems stochastically in the right
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way,
we eventually reach a situation where the
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number
of systems in each configuration remains
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constant
even though any given system keeps
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moving
between configurations
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