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
|
| \begin{equation*} 1 = \sum_{i=1}^W p_i = \frac{1}{Z} \exp\left( - \frac{U}{k T} \right) \sum_{i=1}^W 1 = \frac{1}{Z} \exp\left( - \frac{U}{k T} \right) W \qquad . \end{equation*} | (2.23) |
and
|
| \begin{equation*} S = k \ln(Z) + \frac{1}{T} U = k \ln(W) \qquad . \end{equation*} | (2.24) |
\(W\): Number of the micro states of a system with energies \(U\).
The isolated
system is therefor characterized by \(U = const.\) and \(S = const.\)
|
|
|
|
© J. Carstensen (Stat. Meth.)