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Macrocanonical Partition Function
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Si la funci n partici n para la distribuci n can nica con un n mero fijo de part culas
donde
The average energy is determined with respect to
and can be expressed as follows:
$\bar{E}=-\displaystyle\frac{1}{\sum_re^{-\beta E_r}}\displaystyle\frac{\partial}{\partial\beta}\sum_re^{-\beta E_r}$
This can be summarized as
$\bar{E}=-\displaystyle\frac{1}{Z}\displaystyle\frac{\partial Z}{\partial\beta}$
where we introduce the so-called partition function with
The letter $Z$ originates from the German word Zustandsumme (Zustand=State, Summe=sum).
The partition function is a generating function, meaning it generates other functions that have physical significance.
Con la gran funci n partici n con
se puede calcular nuevamente la energ a media como la derivada en beta del logaritmo de la gran funci n partici n con
En analog a a como se calcula la energ a media derivando el logaritmo de la funci n partici n con
en beta se puede calcular el n mero medio derivando respecto de alfa con
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