Entropy-Order Balance II: Quantum Structure, Measurement, and Decoherence

Any finite-resolution description of a physical system incurs two costs: an information cost, quantifying microscopic complexity via relative entropy, and an ordering cost, quantifying geometric or structural organization. The Entropy–Order Balance (EOB) framework postulates that realized physical laws correspond to Lyapunov-stable equilibria of the total cost functional. Part I showed that the gravitational sector — Einstein's field equations and the cosmological constant — emerges as the stable ordering response. This paper shows that quantum mechanics emerges as the stable information response. Starting from the same five operational axioms applied to resolution windows with smooth Riemannian structure, supplemented by Lyapunov stability and two standard GPT-to-quantum hypotheses (reversible subgroup, local tomography/purification), the paper derives: State-space convexity from variational stability — a result that standard quantum reconstruction programs (Hardy 2001, Chiribella–D'Ariano–Perinotti 2011) assume as a postulate Hilbert space structure and completely positive trace-preserving (CPTP) dynamics Born rule probabilities from decision-theoretic stability over KL divergence Measurement as a barrier-dominance phenomenon: inter-sector transitions in the EOB functional are exponentially suppressed in apparatus size, producing effective state reduction without a collapse postulate A universal decoherence timescale τ_dec = d_S/c depending only on system dimension and the same constant c that determines Λ = cH₀² in Part I Pointer basis selection via Holevo quantity maximization Conditional extensions requiring additional AQFT inputs (Bisognano–Wichmann property, Haag–Kastler net structure) yield an area-law entropy exponent d = 2 and identification of the EOB balance scale with the Planck length. Part I (companion paper) derives Einstein's field equations and the cosmological constant from the same axiomatic framework.