  Equilibration of a one-dimensional system of interacting electrons requires
processes that change the numbers of left- and right-moving particles. At low
temperatures such processes are strongly suppressed, resulting in slow
relaxation towards equilibrium. We study this phenomenon in the case of
spinless electrons with strong long-range repulsion, when the electrons form a
one-dimensional Wigner crystal. We find the relaxation rate by accounting for
the Umklapp scattering of phonons in the crystal. For the integrable model of
particles with inverse-square repulsion, the relaxation rate vanishes.
