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The constant in () can be determined by normalizing
the probability distribution i.e. requiring that
Let us define the canonical partition function
(
We find that the probability
that a state is in a given
microstate

(17) 
Eq. () is the canonical distribution. If
is the value of some physical property in microstate
and
the energy of this state then the canonical
ensemble average is given by

(18) 
Equation () is a very useful formula, and we will give many
examples of its use.
Birger Bergersen
19980914