  In one-dimensional (1D) conductors with linear E-k dispersion (Dirac systems)
intrabranch thermalization is favored by elastic electron-electron interaction
in contrast to electron systems with a nonlinear (parabolic) dispersion. We
show that under external electric fields or thermal gradients the carrier
populations of different branches, treated as Fermi gases, have different
temperatures as a consequence of self-consistent carrier-heat transport.
Specifically, in the presence of elastic phonon scattering, the Wiedemann-Franz
law is restricted to each branch with its specific temperature and is
characterized by twice the Lorenz number. In addition thermoelectric power
vanishes due to electron-hole symmetry, which is validated by experiment.
