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up with very low with very low
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up with very low with very low
probability okay makes sense um the sum
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probability okay makes sense um the sum
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probability okay makes sense um the sum
of all these unnormalized probability
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of all these unnormalized probability
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of all these unnormalized probability
terms is called the partition function
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terms is called the partition function
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terms is called the partition function
and you can show that knowledge of the
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and you can show that knowledge of the
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and you can show that knowledge of the
partition function is exactly the same
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partition function is exactly the same
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partition function is exactly the same
as knowledge of the free energy the free
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as knowledge of the free energy the free
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as knowledge of the free energy the free
energy is essentially the logarithm of
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energy is essentially the logarithm of
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energy is essentially the logarithm of
the partition function and the entropy
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the partition function and the entropy
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the partition function and the entropy
is the product of the probability times
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is the product of the probability times
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is the product of the probability times
the log of the probability summed over
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the log of the probability summed over
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the log of the probability summed over
these things and again that makes sense
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these things and again that makes sense
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these things and again that makes sense
because if you are in one microscopic
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because if you are in one microscopic