Multiplicity of a two state system

  • Thread starter d2x
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  • #1
d2x
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I only have a doubt about which definition to use for the multiplicity of a two state system. Clearly the total multiplicity of a two state system is given by:

[itex]Ω=2^N[/itex],

but what about the definition:

[itex]Ω(N,n) = \binom{N}{n} = \frac{N!}{n!\cdot(N-n)!}[/itex].

Clearly:
[itex]2^N ≠ \frac{N!}{2!\cdot(N-2)!}[/itex].

What is the difference between these two expressions for multiplicity? Is the second one incorrect for a two state system of N things?
Thanks.
 

Answers and Replies

  • #2
3,880
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If you sum the second one over n you get the first one.
 

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