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Thermal
equilibrium is a difficult concept!
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It
does not mean that the system has settled down into the
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lowest
energy configuration.
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The
thing that settles down is the probability
distribution over
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configurations.
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The best way to
think about it is to imagine a huge ensemble of
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systems that all
have exactly the same energy function.
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The
probability distribution is just the fraction of the systems that
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are
in each possible configuration.
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We
could start with all the systems in the same configuration, or
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with
an equal number of systems in each possible configuration.
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After
running the systems stochastically in the right way, we
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eventually
reach a situation where the number of systems in
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each
configuration remains constant even though any given
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system
keeps moving between configurations
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