  It is known that the trajectory of an endoreversibly driven system with
minimal dissipation is a geodesic on the equilibrium state space. Thereby, the
state space is equipped with the Riemannian metric given by the Hessian of the
free energy function, known as Fisher information metric. However, the
derivations given until now require both the system and the driving reservoir
to be in local equilibrium. In the present work, we rederive the framework for
chemical reaction networks and thereby enhance its scope of applicability to
the nonequilibrium situation. Moreover, because our results are derived without
restrictive assumptions, we are able to discuss phenomena that could not been
seen previously. We introduce a suitable weighted Fisher information metric on
the space of chemical concentrations and show that it characterizes the
dissipation caused by diffusive driving, with arbitrary diffusion rate
constants. This allows us to consider driving far from equilibrium. As the main
result, we show that the isometric embedding of a steady state manifold into
the concentration space yields a lower bound for the dissipation when the
system is driven along the manifold. We give an analytic expression for this
bound and for the corresponding geodesic, and thereby are able to dissect the
contributions from the driving kinetics and from thermodynamics. Finally, we
discuss in detail the application to quasi-thermostatic steady states.
