The Universal and Null Attractors: The Impossibility of Absolute Uniformity in Closed Dynamic Systems

The Universal Attractor (UA), a theoretical dynamical rule intended to enforce absolute uniformity (zero relative variance Sc = 0 or zero normalized entropy Sd = 0) under strict impartiality in closed systems, is proven mathematically identical to the Null Attractor (NA), which generates maximal-entropy statistical noise (Sd = 1). This exact UA = NA equivalence entails that perfect order is dynamically inaccessible whenever all elements are treated identically: normalized entropy is strictly bounded to 0 < S < 1, with structural complexity seeded by initial imperfections. The result holds analytically in continuous and discrete frameworks and is confirmed by simulation (N = 100–1000). Escape from the null regime requires bias-induced spontaneous symmetry breaking. Cosmologically, the UA = NA equivalence resolves the boundary-condition problem: a perfectly impartial, exactly symmetric initial state is dynamically forbidden; unavoidable quantum fluctuations enforce the null attractor from the Planck epoch, and the observed large-scale cosmic order and gravitational entropy gradient arise via spontaneous symmetry breaking seeded by irreducible ground-state noise. Full cosmological implications are developed in Ref. [15].