We extend Onsager's minimum dissipation principle to stationary states that
are only subject to local equilibrium constraints, even when the transport
coefficients depend on the thermodynamic forces. Crucial to this generalization
is a decomposition of the thermodynamic forces into those that are held fixed
by the boundary conditions, and the subspace which is orthogonal with respect
to the metric defined by the transport coefficients. We are then able to apply
Onsager and Machlup's proof to the second set of forces. As an example we
consider two-dimensional nonlinear diffusion coupled to two reservoirs at
different temperatures. Our extension differs from that of Bertini et al. in
that we assume microscopic irreversibility and we allow a nonlinear dependence
of the fluxes on the forces.Comment: 20 pages, 1 figur