  We consider a system of one-dimensional spinless particles interacting via
long-range repulsion. In the limit of strong interactions the system is a
Wigner crystal, with excitations analogous to phonons in solids. In a harmonic
crystal the phonons do not interact, and the system never reaches thermal
equilibrium. We account for the anharmonism of the Wigner crystal and find the
rate at which it approaches equilibrium. The full equilibration of the system
requires umklapp scattering of phonons, resulting in exponential suppression of
the equilibration rate at low temperatures.
