  The Bloch theorem is a general theorem restricting the persistent current
associated with a conserved U(1) charge in a ground state or in a thermal
equilibrium. It gives an upper bound of the magnitude of the current density,
which is inversely proportional to the system size. In a recent paper, Else and
Senthil applied the argument for the Bloch theorem to a generalized Gibbs
ensemble, assuming the presence of an additional conserved charge, and
predicted a nonzero current density in the nonthermal steady state [D. V. Else
and T. Senthil, Phys. Rev. B 104, 205132 (2021)]. In this work, we provide a
complementary derivation based on the canonical ensemble, given that the
additional charge is strictly conserved within the system by itself.
Furthermore, using the example where the additional conserved charge is the
momentum operator, we discuss that the persistent current tends to vanish when
the system is in contact with an external momentum reservoir in the co-moving
frame of the reservoir.
