  The damping of primordial perturbations at small scales gives rise to
distortions of the cosmic microwave background (CMB). Here, the dependence of
the distortion on the different types of cosmological initial conditions is
explored, covering adiabatic, baryon/cold dark matter isocurvature, neutrino
density/velocity isocurvature modes and some mixtures. The radiation transfer
functions for each mode are determined and then used to compute the dissipative
heating rates and spectral distortion signatures, utilizing both analytic
estimates and numerical results from the thermalization code CosmoTherm. Along
the way, the early-time super-horizon behavior for the resulting fluid modes is
derived in conformal Newtonian gauge, and tight-coupling transfer function
approximations are given. CMB spectral distortions caused by different
perturbation modes can be estimated using simple k-space window functions which
are provided here. Neutrinos carry away some fraction of the primordial
perturbation power, introducing an overall efficiency factor that depends on
the perturbation type. It is shown that future measurements of the CMB
frequency spectrum have the potential to probe different perturbation modes at
very small scales (corresponding to wavenumbers 1 Mpc^{-1} < k < few x 10^4
Mpc^{-1}). These constraints are complementary to those obtained at large
scales and hence provide an exciting new window to early-universe physics.
