  The isothermal compressibility of a general crystal is analyzed within
classical density functional theory. Our approach can be used for homogeneous
and unstrained crystals containing an arbitrarily high density of local
defects. We start by coarse-graining the microscopic particle density and then
obtain the long wavelength limits of the correlation functions of elasticity
theory and the thermodynamic derivatives. We explicitly show that the long
wavelength limit of the microscopic density correlation function differs from
the isothermal compressibility. It also cannot be obtained from the static
structure factor measured in a scattering experiment. We apply our theory to
crystals consisting of soft particles which can multiply occupy lattice sites
('cluster crystals'). The multiple occupancy results in a strong local disorder
over an extended range of temperatures. We determine the cluster crystals'
isothermal compressibility, the fluctuations of the lattice occupation numbers
and their correlation functions, and the dispersion relations. We also discuss
their low-temperature phase diagram.
