  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.
