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I posted this once already without seeing the rule that HW questions must go here--sorry

So, the problem: I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be:

ε / (e^βε + 1) , where β is thermodynamic beta, 1/KbT.

How do I convert this to an expression for the variance of the energy?

A more complete description of the problem can be found http://books.google.com/books?id=z6P7wP9zwcYC&printsec=frontcover&dq=Concepts+in+thermal+physics&cd=1#v=onepage&q=&f=false", on the top half of page 41:

I've already found http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Relation_to_thermodynamic_variables" explanation, but I'm not connecting how it could be applied to this example:

Please, can anyone point me in the right direction?

So, the problem: I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be:

ε / (e^βε + 1) , where β is thermodynamic beta, 1/KbT.

How do I convert this to an expression for the variance of the energy?

A more complete description of the problem can be found http://books.google.com/books?id=z6P7wP9zwcYC&printsec=frontcover&dq=Concepts+in+thermal+physics&cd=1#v=onepage&q=&f=false", on the top half of page 41:

I've already found http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Relation_to_thermodynamic_variables" explanation, but I'm not connecting how it could be applied to this example:

Please, can anyone point me in the right direction?

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