  We analyze the role of the surface terms in the conservation law for the sum
of the magnetic helicity density and the chiral imbalance of the charged
particle densities. These terms are neglected in the Anomalous
MagnetoHydroDynamics (AMHD), where infinite volume is considered typically. We
discuss a finite volume system, such as a magnetized neutron star (NS), and
study the contribution of the surface terms to the evolution of the magnetic
helicity. Accounting for the fast washing out of the chiral imbalance in a
nascent NS, we demonstrate that the surface terms contribution can potentially
lead to the reconnection of magnetic field lines and subsequent gamma or X-ray
bursts observed from magnetars. We derive the additional surface terms
originated by the mean spin flux through a volume boundary arising due to
macroscopic spin effects in electron-positron plasma. Then, comparing this
quantum surface term with the classical one known in standard MHD, we find that
the new quantum contribution prevails over classical term for the rigid NS
rotation only.
