  We study equilibration of an isolated quantum system by mapping it onto a
network of classical oscillators in Hilbert space. By choosing a suitable basis
for this mapping, the degree of locality of the quantum system reflects in the
sparseness of the network. We derive a Lieb-Robinson bound on the speed of
propagation across the classical network, which allows us to estimate the
timescale at which the quantum system equilibrates. The bound contains a
parameter that quantifies the degree of locality of the Hamiltonian and the
observable. Locality was disregarded in earlier studies of equilibration times,
and is believed to be a key ingredient for making contact with the majority of
physically realistic models. The more local the Hamiltonian and observables,
the longer the equilibration timescale predicted by the bound.
