Generalized entropy formulation of dissipative magnetohydrodynamics

A variational-principle formulation of dissipative magnetohydrodynamics (DMHD) including thermal conduction and viscous dissipation as well as resistive decay is presented. The functional to be minimized is an extension of the generalized entropy-production (GEP) rate first discussed by I. Prigogine 2 [Nonequilibrium Thermodynamics, Variational Techniques, and Stability, edited by R. J. Donnelly, R. Herman, and I. Prigogine (University of Chicago Press, Chicago, 1966)]. Minimization of this functional at each instant of time results in the proper evolutionary behavior of the MHD fields while the correct boundary conditions are maintained. Steady-state solutions are obtained as a special case of the GEP functional minimization, which is fully consistent with earlier entropy formulations for the steady state. The method is illustrated with an explicit application to a simple, one-dimensional model of a reversed-field pinch.