  We establish a relation between two hallmarks of integrable systems: the
relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless
charge transport. We show that the former one is possible only if the so called
Mazur bound on the charge stiffness is saturated by local conserved quantities.
As an example we show how a non--GGE steady state with a current can be
generated in the one-dimensional model of interacting spinless fermions with a
flux quench. Moreover an extended GGE involving the quasi-local conserved
quantities can be formulated for this case.
