The derivatives of some of the functions plotted in the various chapters with respect to the parameters of the Hamiltonian, external fields, coupling strengths, and temperature, are of interest because they are related to correlations of statistical variables in the systems described. These correlations are averages over the possible states of the system using the calculated equilibrium distribution. Such averages must therefore implicitly ignore any dynamics. However, for a system in thermodynamic equilibrium at a given temperature exhibiting stationary ergodic dynamics, the average of a system variable using the equilibrium distribution is equivalent to the time average of the system variable. We can go further. It is shown next that if there is a dynamics, the inverse Fourier transform of the product of the amplitude spectra of two system variables is the equilibrium distribution time-dependent correlation of those system variables. When the time between the two chosen system variables is taken to be zero, we immediately have that the average power in the spectrum of a system variable is equal to the equilibrium distribution correlation. In this manner it is possible to get a connection between the time average behavior of a system and equilibrium derivatives. The connection is best presented by way of the Weiner-Khinchin theorem [27], described next.