The thermodynamic dual structure of linear-dissipative driven systems

The spontaneous emergence of dynamical order, such as persistent currents, is sometimes argued to require principles beyond the entropy maximization of the second law of thermodynamics. I show that, for linear dissipation in the Onsager regime, current formation can be driven by exactly the Jaynesian principle of entropy maximization, suitably formulated for extended systems and nonequilibrium boundary conditions. The Legendre dual structure of equilibrium thermodynamics is also preserved, though it requires the admission of current-valued state variables, and their correct incorporation in the entropy.