  We challenge claims that the principle of maximum entropy production produces
physical phenomenological relations between conjugate currents and forces, even
beyond the linear regime, and that currents in networks arrange themselves to
maximize entropy production as the system approaches the steady state. In
particular: (1) we show that Ziegler's principle of thermodynamic orthogonality
leads to stringent reciprocal relations for higher order response coefficients,
and in the framework of stochastic thermodynamics, we exhibit a simple explicit
model that does not satisfy them; (2) on a network, enforcing Kirchhoff's
current law, we show that maximization of the entropy production prescribes
reciprocal relations between coarse-grained observables, but is not responsible
for the onset of the steady state, which is rather due to the minimum entropy
production principle.
