In this paper we deal with weak solutions to the Maxwell-Landau-Lifshitz
equations and to the Hall-Magneto-Hydrodynamic equations. First we prove that
these solutions satisfy some weak-strong uniqueness property. Then we
investigate the validity of energy identities. In particular we give a
sufficient condition on the regularity of weak solutions to rule out anomalous
dissipation. In the case of the Hall-Magneto-Hydrodynamic equations we also
give a sufficient condition to guarantee the magneto-helicity identity. Our
conditions correspond to the same heuristic scaling as the one introduced by
Onsager in hydrodynamic theory. Finally we examine the sign, locally, of the
anomalous dissipations of weak solutions obtained by some natural approximation
processes.Comment: 45 page
