  In the last few decades, some hypotheses for entropy production (EP)
principles have been forwarded as possible candidates for organizational
principles in non-linear non- equilibrium systems. Two important hypotheses
will be studied: the maximum entropy production (MaxEP) principle that claims
that the selected steady state has the highest EP, and the gradient response
principle that claims that the EP of the selected steady state (maximally)
increases when the external thermodynamic driving force increases. We will
formulate these hypotheses more rigorously and present a simple chemical
reaction model to test these hypotheses. With the help of this model, we will
clearly demonstrate that there are different MaxEP hypotheses being discussed
in the literature and we will look at some parts in the literature where these
differences are not always clarified. Furthermore, our chemical model will be a
general counter example to all of these MaxEP and gradient response hypotheses.
