  We study the ratio of the energy and particle currents ($j^E/j^N$) in an
integrable one dimensional system of interacting fermions. Both currents are
driven by a finite (nonzero) dc electric field. In doped insulators, where the
local conserved quantities saturate the so called Mazur bound on the charge
stiffness, $j^E/j^N$ agrees with the linear--response theory, even though such
agreement may be violated for each current alone. However, in the metallic
regime with a non-saturated Mazur bound, the ratio $j^E/j^N$ in a driven system
is shown to be much larger than predicted by the linear--response theory.

Strongly Correlated Electrons