Thermodynamic Derivation of Born's Rule and Extensions of Complexity Binding Theory to Quantum and Black Hole Regimes

This paper extends Complexity Binding Theory (CBT) from galactic dynamics to quantum mechanics and black hole physics. I demonstrate that Born's probability rule P = |ψ|² emerges naturally from entropy maximization in the binding field framework, without requiring it as an axiom. Entanglement entropy is identified with binding entropy, providing a unified information-theoretic interpretation. The binding field is shown to saturate at event horizons, recovering Bekenstein-Hawking entropy. Additionally, I explore a heuristic connection between the galactic binding parameter α₀ = 1/e and quantum decoherence scales, yielding predictions consistent with experimental coherence times in superconducting qubits and trapped ions. This work suggests that quantum probability, entanglement, decoherence, and black hole thermodynamics may share a common entropic origin through a single scalar binding field. Keywords: quantum foundations, Born's rule, decoherence, black hole entropy, complexity, entropic gravity