Calculation of the microcanonical ensemble

2.4 Calculation of the microcanonical ensemble

In the microcanonical ensemble we only sum up micro states $p_{i}$ with energies $U_{i} = U$ . The remaining $p_{i}$ are zero.
We find

$1 = \sum_{i = 1}^{W} p_{i} = \frac{1}{Z} exp (- \frac{U}{k T}) \sum_{i = 1}^{W} 1 = \frac{1}{Z} exp (- \frac{U}{k T}) W .$

(2.23)

and

$S = k ln (Z) + \frac{1}{T} U = k ln (W) .$

(2.24)

$W$ : Number of the micro states of a system with energies $U$ .
The isolated system is therefor characterized by $U = c o n s t .$ and $S = c o n s t .$

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