drive the system to resonance, and the gradual adjustment of the dipole fields in the sample caused by tunnelling, brings other clusters into resonance and allows a continuous relaxation. Hence the observation of relaxation in single molecule magnets is fundamentally dependent on the hyperfine coupling with the fields of nuclear spins [@Wernsdorfer00].

The Prokof’ev and Stamp model [@PS] certainly does not apply in detail to spin ice at low temperatures. First, in single molecule magnets the spin of any particular complex in the system is available to be brought to resonance, whereas in spin ice, only those spins that are instantaneously associated with a diffusing monopole are available to tunnel (and this presumes that more extended excitations can be neglected). The remaining spins – the vast majority – are, in contrast, static and instantaneously ordered by the ice rules. The rate of flipping of these quasi-ordered spins, which corresponds to monopole pair creation, is negligible at the temperatures studied and the process is not relevant to our experiments. Thus, even at equilibrium, spin ice has an effective number of flippable spins that depends on temperature (see Supplementary Fig. 1). Away from equilibrium, where our experiments are performed, the number of 