  Here we calculate the dynamic susceptibility and dynamic correlation function
in spin ice using the model of emergent magnetic monopoles. Calculations are
based on a method originally suggested for the description of dynamic processes
in water ice (non-equilibrium thermodynamics approach). We show that for zero
temperature the dynamic correlation function reproduces the transverse dipole
correlations (static correlation function) characteristic of spin ice in its
ground state. At non-zero temperatures the dynamic correlation function
includes an additional longitudinal component which decreases as the
temperature decreases. Both terms (transverse and longitudinal) exhibit
identical Debye-like dependences on frequency but with different relaxation
times: the magnetic Coulomb interaction of monopoles reduces the longitudinal
relaxation time with respect to the transverse one. We calculate the dielectric
function for the magnetic monopole gas and discuss how the non-equilibrium
thermodynamics approach exposes corrections to the Debye-Huckel theory of
magnetic monopoles and the concept of "entropic charge".
