  Bloch theorem states the impossibility of persistent electric currents in the
ground state of nonrelativistic fermion systems. We extend this theorem to
generic systems based on the gauged particle number symmetry and study its
consequences on the example of chiral transport phenomena. We show that the
chiral magnetic effect can be understood as a generalization of the Bloch
theorem to a nonequilibrium steady state, similarly to the integer quantum Hall
effect. On the other hand, persistent axial currents are not prohibited by the
Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic
matter. An application of the generalized Bloch theorem to quantum time
crystals is also discussed.
