This paper restates and extends, as the V7 revision of an earlier framework, an interpretive–diagnostic account of the macroscopic behavior of open, flux-carrying systems. The central organizing statement is renamed from the Law of Nonuniformity to the Principle of Nonuniformity and is recast as a first principle for open systems: the state of an open system deviates from uniformity in both space and time, and this deviation is structural — non-ergodic and accumulable — rather than a mere fluctuation. The dividing criterion between fluctuation and structure is ergodicity breaking (ensemble average ≠ time average). We make the principle’s domain precise by isolating the one regime it does not govern, the ergodic equilibrium floor (the U = 0 baseline), and by explaining why uniformity is the exception at every scale — the universe included — while the principle is stated for open systems. On this footing we retain and develop the quantitative apparatus. Using relative entropy we define two nonequilibrium potentials: Uᵤnif, referenced to the uniform distribution, for closed (state-count-conserving) systems; and Uₑxp, referenced to the same-mean exponential distribution, for open (flux-conserving) systems. Under a mean constraint the exponential law is the maximum-entropy distribution and is therefore the geometric zero of open systems. To offset an ordering quantity against work we introduce an energy-dimensioned ordered free energy 𝒰 ≡ kB·T_*·Uₑxp, and write a dimensionally consistent master equation for the evolution of order together with its three-variable coupling to activity and work rate, yielding a maintenance fixed point, a fossil state, a minimum maintenance power, and a critical margin. We clarify the variational status of the dynamics: a single-coordinate relaxation is always an identity rewriting as a gradient flow with no independent physical content; the genuinely falsifiable structural claim is multivariate detailed balance, and the full three-way coupled system generically breaks it, retaining only a weak quasipotential variational structure. The fluctuation theorem yields a second law for open systems whose compact form is a nonpositive free-energy dissipation rate, equivalent to nonnegative internal entropy production. We further give: a dimensionless number distinguishing static from Red-Queen dynamic steady states, with an observable scaling law; a spatial gradient-surplus principle in which a single screening-length knob interpolates between exponential and power-law profiles — dissipation compresses the profile to an exponential while vanishing dissipation opens it to a power law; a policy result — uniform additive intervention cannot prevent multiplicative power-law concentration, and suppressing heavy tails requires acting on the multiplicative growth channel; and an ontological ordering of phase transitions — the exponential first-order transition is primal in the zero-constraint limit, while the power-law second-order transition is a secondary form shaped by external constraints. Throughout we separate borrowed mathematical tools from the framework’s own diagnostic conclusions, and give falsifiable test points.
Qinfu Li (Mon,) studied this question.