Branch selection in driven steady states is set by the full contracted action, not the dissipation rate alone

Plain-language summary. Many driven systems — chemical mixtures, swarms of active particles, even the climate — can settle into any of several steady patterns. A popular idea holds that the winner is picked by dissipation: the pattern that dissipates fastest, or that absorbed the most work along the way, is the one selected. This intuition underlies the “dissipative adaptation” view of self-organization and the “maximum entropy production” (MEP) principle. This paper shows that, in general, the dissipation rate alone does not decide the outcome. In the standard mathematics of stochastic thermodynamics, the quantity that ranks the competing steady states — a kind of path “action” — splits into three parts: the entropy production (the piece tied to the arrow of time), a time-symmetric piece measuring how busy the dynamics are, and a boundary piece (fixed by where the paths start and end). The entropy production is only one of the three, and the other two are not fixed by it. A small, exactly solvable model makes this concrete: a single “hot spot” placed inside one of two wells — a discrete version of Landauer’s classic “blowtorch.” The entropy production for crossing between the wells is exactly zero, yet the populations of the wells still shift, and a symmetric version of the model even reverses which well is favored. So a rule based on the dissipation rate alone can give the wrong answer, not merely an incomplete one. Four independent results already in the literature — a pair of dissipative quantum systems, fine-tuning in random chemical reaction networks, an internal no-go for a proposed dissipation bound on replicators, and the “low-rattling” principle — fit the same pattern. The conclusion is constructive, not merely negative. Entropy production is indispensable, but it is not a universal selector. Both popular principles survive as conditional statements: each holds when an extra, model-specific condition (a “closure”) lines the dissipation up with the true ranking, and typically fails when it does not. The object to track is the full action — entropy production together with the time-symmetric and boundary parts — not the dissipation rate by itself. Why it matters. “Dissipative adaptation” and “maximum entropy production” are used as rules of thumb for predicting how driven and lifelike systems organize, across active matter, origin-of-life research, and Earth-system science. This work marks where such a rule can be trusted: it pinpoints exactly what the dissipation rate leaves out, gives a transparent counterexample in which the rate points the wrong way, and recasts the popular principles as precise, checkable conditions rather than universal laws — clarifying when they can be relied on, and what must be added when they cannot.