A thermodynamic model is developed for plasma systems that are forced to carry an electrical current which prevents relaxation into global thermodynamic equilibrium. Complementary to earlier approaches in the framework of resistive magnetohydrodynamics, the role of nonresistive dissipation is analyzed by excluding momentum transfer between different particle species (electrons and ions). The general class of steady states compatible with the assumptions is found and their structures and symmetries are discussed. The second law of thermodynamics guarantees the existence of a generalized thermodynamic potential (including contributions of the electromagnetic field) which has a negative time derivate for all dynamical states subject to the equilibrium symmetry and boundary conditions. Applying Lyapunov’s theory, this functional provides a necessary and sufficient stability criterion. The linearized version of this criterion and the corresponding eigenvalue problem are also derived.