  We consider one-dimensional (1D) interacting electrons beyond the
Dzyaloshinskii-Larkin theorem, i.e., keeping forward scattering interactions
among the electrons but adding a non-linear correction to the electron
dispersion relation. The latter generates multi-loop corrections to the
polarization operator and electron self-energy thereby providing a variety of
inelastic processes affecting equilibrium as well as non-equilibrium properties
of the 1D system. We first review the computation of equilibrium properties,
e.g., the high frequency part of the dynamical structure factor and corrections
to the electron-electron scattering rate. On this basis, microscopic
equilibration processes are identified and a qualitative estimate of the
relaxation rate of thermal carriers is given.
