  The maximum entropy principle (MEP) apparently allows us to derive, or
justify, fundamental results of equilibrium statistical mechanics. Because of
this, a school of thought considers the MEP as a powerful and elegant way to
make predictions in physics and other disciplines, which constitutes an
alternative and more general method than the traditional ones of statistical
mechanics. Actually, careful inspection shows that such a success is due to a
series of fortunate facts that characterize the physics of equilibrium systems,
but which are absent in situations not described by Hamiltonian dynamics, or
generically in nonequilibrium phenomena. Here we discuss several important
examples in non equilibrium statistical mechanics, in which the MEP leads to
incorrect predictions, proving that it does not have a predictive nature. We
conclude that, in these paradigmatic examples, the "traditional" methods based
on a detailed analysis of the relevant dynamics cannot be avoided.
