TEMPORAL SUSCEPTIBILITY AND THE KYIV–OHNISHI FLOW: A LIE-ALGEBRAIC FRAMEWORK FOR DISSIPATIVE QUANTUM DYNAMICS

Abstract

The standard theory of quantum decoherence treats the environment as an external reservoir imposing a fixed decoherence rate. We propose a fundamental reinterpretation: within the Lie-Observable-Dependent Renormalization (LA-ODR) framework, the decoherence rate Γτ = Γ₀(χτ)^β is governed by the temporal susceptibility χτ — a state-dependent order parameter of phase-ensemble desynchronization. We derive the Kyiv–Ohnishi hybrid flow dχτ/dt = -αΓ₀(χτ)^(β+1) - λ_ctrlχτ + λ_nat(1-χτ), establish four theorems of global asymptotic stability via Lyapunov analysis, and prove a triple algebraic–geometric–thermodynamic correspondence at the fixed point χτ* = λ_nat/(λ_ctrl + λ_nat). The effective state-space metric dsτ² = (1-χτ)c²dt² - (1+χτ)dx² is a Riemannian analogue of the Fubini–Study metric on susceptibility space, not a physical spacetime metric. The framework provides the mathematical foundation for active coherence control in NISQ quantum devices.