Aharonov-Bohm magnetization of mesoscopic rings caused by inelastic   relaxation
  The magnetization of a system of many mesoscopic rings under non-equilibrium conditions is considered. The corresponding disorder-averaged current in a ring is shown to be a sum of the `thermodynamic' and `kinetic' contributions both resulting from the electron-electron interaction. The thermodynamic part can be expressed through the diagonal matrix elements of the current operator in the basis of exact many-body eigenstates and is a generalization of the equilibrium persistent current. The novel kinetic part is present only out of equilibrium and is governed by the off-diagonal matrix elements. It has drastically different temperature and magnetic field behavior. 
O.L.Chalaev and V.E.Kravtsov