When can maximum entropy production select a branch? Frenesy, quasi-potentials, and closure conditions

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 This manuscript has not been peer reviewed.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