  When degenerate states are separated by large energy barriers, the approach
to thermal equilibrium can be slow enough that physical properties are defined
by the thermalization process rather than the equilibrium. The exploration of
thermalization pushes experimental boundaries and provides refreshing insights
into atomic scale correlations and processes that impact steady state dynamics
and prospects for realizing solid state quantum entanglement. We present a
comprehensive study of magnetic relaxation in Ho$_2$Ti$_2$O$_7$ based on
frequency-dependent susceptibility measurements and neutron diffraction studies
of the real-time atomic-scale response to field quenches. Covering nearly ten
decades in time scales, these experiments uncover two distinct relaxation
processes that dominate in different temperature regimes. At low temperatures
(0.6K<T<1K) magnetic relaxation is associated with monopole motion along the
applied field direction through the spin-ice vacuum. The increase of the
relaxation time upon cooling indicates reduced monopole conductivity driven by
decreasing monopole concentration and mobility as in a semiconductor. At higher
temperatures (1K<T<2K) magnetic relaxation is associated with the reorientation
of monopolar bound states as the system approaches the single-spin tunneling
regime. Spin fractionalization is thus directly exposed in the relaxation
dynamics.
