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It can be shown that the value of [E - TS]N calculated in the grand canonical ensemble is equal to the Helmholtz free energy per particle calculated in the canonical ensemble if the value of N is very large. This equivalence of ensembles is not present for small N because Stirlings approximation involved in the transformation between the two ensembles is valid only for large value of N
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It can be shown that the value of [E - TS]N calculated in the grand canonical ensemble is equal to the Helmholtz free energy per particle calculated in the canonical ensemble if the value of N is very large. This equivalence of ensembles is not present for small N because Stirlings approximation involved in the transformation between the two ensembles is valid only for large value of N.
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