  One-dimensional electrons with a linearized dispersion relation are
equivalent to a collection of harmonic plasmon modes, which represent long
wavelength density oscillations. An immediate consequence of this Luttinger
model of one-dimensional electron systems is the absence of inelastic
scattering processes responsible for the relaxation of nonequilibrium states.
In a generic nonlinear Luttinger liquid plasmons may decay and thus acquire a
finite lifetime. We show that equilibration of plasmons is hierarchical and has
profound implications for the dynamics after a thermal quench. We also develop
a thermal transport theory and compute thermal conductance of the nonlinear
Luttinger liquid by treating the collision integral of plasmons in a manifestly
nonperturbative way.
