https://ens.hal.science/hal-02175571Coquinot, BaptisteBaptisteCoquinotFRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueMorrison, PhilipPhilipMorrisonIFS - Institute for Fusion Studies - University of Texas at Austin [Austin]University of Texas at Austin [Austin]A General Metriplectic Framework with Application to Dissipative Extended MagnetohydrodynamicsHAL CCSD2019Fluid DynamicsHamiltonian DynamicsNon-Equilibrium Thermody- namicsPlasma PhysicsDissipative Extended MagnetohydrodynamicsMetriplectic Brackets[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph][PHYS.PHYS.PHYS-FLU-DYN] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn][PHYS.PHYS.PHYS-PLASM-PH] Physics [physics]/Physics [physics]/Plasma Physics [physics.plasm-ph]Coquinot, Baptiste2019-07-05 19:24:102023-03-24 14:53:112019-07-10 10:35:49enPreprints, Working Papers, ...https://ens.hal.science/hal-02175571/document10.1017/S0022377820000392application/pdf1General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model have already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view for deriving dissipative brackets, a means of derivation that is natural for understanding and creating dissipative brackets. Finally the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, nonlocal dissipative brackets naturally emerge.