Dissipative effects in magnetohydrodynamical models with intrinsic magnetization

•Non-canonical Hamiltonian formulation of magnetohydrodynamic models with magnetization described.•Connections with spin-1/2 MHD theory of quantum plasmas highlighted.•Metriplectic dynamics accounting for dissipative effects in these models presented.•Entropy production occurs via novel magnetization-driven term.

A unifying non-canonical Poisson bracket has been shown to describe magnetohydrodynamic models of classical and quantum–mechanical fluids with intrinsic magnetization (or spin), and the Jacobi identity for this bracket is also proven. Their corresponding Hamiltonians are presented, and some interesting features, such as the potential absence of angular momentum conservation, are pointed out. To maintain consistency with the first and second laws of thermodynamics, a metriplectic approach to these models is highlighted which involves entropy production via a hitherto unstudied term involving the magnetization. A few promising avenues and outstanding issues for future work in this area are also discussed.