  Here it is shown 1) how isocurvature inhomogeneities correlated on causally
disconnected (super-horizon) scales are generated from curvature
inhomogeneities which are known to be correlated on these scales 2) that
super-horizon isocurvature generation is nearly inevitable for non-equilibrium
chemical processes 3) that the amplitude of the compositional isocurvature
correlations a) can be large for production of rare objects, b) falls off
rapidly with separation c) falls off at scales below the horizon when these
modes are generated. These two fall-offs results in an "isocurvature bump" in
the power spectrum. Isocurvature generation is illustrated by the process of
dark matter freeze-in, computed here with both separate universe modelling and
linear perturbation theory. For freeze-in the most prominent isocurvature modes
are inhomogeneities in the ratio of dark matter to standard model matter. Much
smaller inhomogeneities in the ratio of baryons to standard model entropy are
also produced. Previous constraints on freeze-in from Ly-$\alpha$ clouds limit
the bump enhancement to $\lesssim10\%$ on comoving scales $\lesssim1\,$Mpc.
Current observations are not sensitive to the isocurvature modes generated in
viable freeze-in models. Results are obtained using a somewhat novel framework
to describe cosmological inhomogeneities.
