Preprint. This manuscript has not been peer reviewed. The upload includes the main manuscript and supplemental material. This paper examines when maximum entropy production (MEP) can, and cannot, serve as a branch-selection principle for nonequilibrium steady states. Branch selection is formulated through the full contracted path action and quasi-potential. Two thermodynamically consistent finite-state counterexamples show that entropy-production ordering alone does not define a universal variational selection rule. Data and code for reproducing the results are available from Mendeley Data:10.17632/pgstrtnwj8
Shigeo Kaneko (Fri,) studied this question.