Limitation of the Number of Degrees of Freedom in Fluctuation Analysis

The limitation on the effective number of degrees of freedom ($N_{\mathrm{eff}}$) due to the possibility that a finite number of statistically independent terms makes up the different amplitudes is considered. A general simple model is considered which leads to a simple expression for $N_{\mathrm{eff}}$. A more detailed calculation is made in which it is assumed that independence is associated only with different values of $J$ and $\pi$. This last calculation is shown to give some improvement over previous calculations.