Three energetic quantities that must not be conflated: amount, gradient and steadiness of flux, the withdrawal of a universal principle of regime selection, and a transferred form of non-monotonic dependence

Preprint, 24 August 2026. A version of this manuscript is under consideration at a peer-reviewed journal of statistical physics. This record carries no peer-review status. Abstract. The assertion “more energy, more order” cannot be tested until it is said which of three distinct quantities is meant by “more”. This paper separates them operationally: the amount of energy delivered over a period; the gradient, a potential difference per unit distance; and the steadiness of the flux, defined here as the coefficient of variation of the intervals between arrivals of energy, denoted R. Two systems receiving the same total energy — one in an erratic sequence of deliveries, the other evenly — occupy different points of the control space, so that any claim indexed only to the total is compatible with both outcomes and therefore excludes nothing. The paper then withdraws a universal principle of regime selection which its own earlier edition had asserted, namely that a system takes the path of least energetic resistance. The ground for withdrawal is the domain of proof rather than caution: the theorem of minimum entropy production is established for steady states in the linear regime near equilibrium, which is not where dissipative structures live, and proposals for extremal principles far from equilibrium have no settled status. In its place a formulation is adopted that obliges measurement: which of the admissible regimes is realised is fixed by the conditions and the history of the system, not by a universal minimum. Finally, from an established and reproducible case — a fluid layer heated from below — the form of the paper’s central testable claim is transferred: the proportion of systems reaching an ordered regime is expected to depend non-monotonically on the intensity of driving, with a threshold and a peak. The transfer of a form is declared to be a transfer and not a derivation, and the conditions under which it would be refuted are named in advance: no fewer than five levels of the control parameter and a comparison of two pre-declared models, monotonic-with-saturation against single-peaked.