Binding Energy, Critical Radii, & Information Maintenance Tax

This paper proposes that binding energies across all scales—nuclear, electromagnetic, gravitational—represent ongoing thermodynamic maintenance costs against entropy, following from Landauer's principle (E = k_B T ln 2 per bit). The framework predicts force-specific "bankruptcy radii" where maintenance equals total energy: QCD confinement at ~1 fm, electromagnetic at the classical electron radius (~2.8 × 10⁻¹⁵ m), and gravitational at the Schwarzschild radius. A complexity multiplier M(η,d) = φ^{2^{d-2}} × (1-η)^{-ρ*} quantifies organizational overhead, where ρ* ≈ 3.29 is the proposed universal exponent. White dwarf trajectories toward the Chandrasekhar limit provide empirical test. We analyze the complete trajectory from stable configurations (η ~ 0.07) to collapse (η ~ 0.97), finding geometric compression increases by factor 2.2 while organizational complexity explodes by factor 2200—a 1000-fold disparity suggesting information bankruptcy drives instability. Independent analysis of the Montreal White Dwarf Database (5,519 objects) and Gaia DR3 (7,496 objects) identifies R/R_S ≈ 10³ as a discrete phase transition boundary, with anomaly-zone objects appearing systematically older than matched references (+103 Myr, p = 0.0025; +58 Myr, p < 0.0001)—consistent with accelerated entropy production upon crossing the threshold. The framework yields a quantitative prediction: Type Ia supernova energy equals the Landauer cost of reorganizing phase space information from electron to neutron degeneracy. Counting bits (ΔN ≈ 4.5 × 10⁵⁸) at shock temperature (T ~ 10⁹ K) gives E = 4.3 × 10⁴⁴ J—matching observed supernova energies. This exact correspondence, if not coincidental, validates that binding encodes maintenance costs. Additional predictions include gravitational wave memory effects from information topology reorganization, primordial black hole equilibrium at lunar mass, and quantum computing limits scaling with R_S/R. The biological efficiency ceiling at η ~ 0.1 (consistent with brain metabolism) suggests universal constraints on self-organizing systems. The interpretation—binding as thermodynamic tax—is speculative but generates falsifiable predictions across 57 orders of magnitude from particles to galaxies.

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