Homeostatic Convergence: Conservative Field Theory as a Unifying Framework for Quantum Coherence, Biological Vitality, and AI Safety Distinguishing Regulated Equilibrium from Perpetual Motion in Complex Systems

ABSTRACTDissipative models dominate complexity science, treating living and intelligent systems asfundamentally entropy-producing structures maintained far from equilibrium throughcontinuous energy throughput. While powerful, this framing obscures a complementarymathematical structure: the conservative field condition, where the closed-loop integral of asystem's state-governing field vanishes. We propose that this condition—formalised as theHomeostatic Boundary Integral (HBI), where the contour integral over the boundary of theregulated domain ∂Ω of the homeostatic field H(x,t) · dx = 0—provides a unifyingmathematical language for coherence across quantum, biological, and artificial intelligencesystems. Critically, we distinguish this formalism from 'unitary flow' interpretations (cf.Neveu, 2024) that risk vitalist overreach by neglecting boundary conditions. Our centralcontribution is the Homeostatic Drift Integral (HDI): the absolute value of the contourintegral, whose exceedance of a critical threshold εc defines a phase transition from coherentto pathological states. We demonstrate cross-domain isomorphism across quantumdecoherence, allostatic load, AI alignment drift, and ecological regime shifts. The frameworkgenerates measurable safety criteria for AI deployment, quantum error correction, andecological governance, grounded in the principle that homeostasis is not the absence of decaybut the active regulation of the boundary within which coherence holds.Keywords: Homeostasis; Conservative Fields; AI Safety; Quantum Coherence; Trust Frameworks;Boundary Regulation; Systemic Risk; Glass Box AI; Decoherence; Allostatic Load; HATI Framework