Thermodynamic Advantage of Transient Wave Dynamics in Hierarchical Decision Architectures: A Lindblad Formalism Approach

Biological agents performing approximate Bayesian inference face a strict metabolic trade-off: minimizing variational free energy requires exploring large hypothesis spaces, yet the energetic cost of classical neuronal signaling (action potentials and global broadcast communication) makes exhaustive search infeasible. We propose Quantum-Resonant Netting (QRN), a dual-stage selection architecture in which a low-cost “wave layer” performs transient pre-selection over a hypothesis graph before an irreversible, spike-based fixation/readout step. Formally, we model the wave layer as open wave dynamics on a graph governed by a Gorini– Kossakowski–Sudarshan–Lindblad (GKSL) generator with coherent transport (γ), local dephasing noise (κ), and irreversible capture into a sink/readout state (η), with a diagonal potential V̂ encoding a local prediction-error (free-energy proxy). Hnet = −γ L + V̂ To make the “optimal noise” claim horizon-independent, we compute the Liouvillian spectral gap g(γ,κ), which controls the asymptotic relaxation time τrelax ≈ 1/g. The ridge of maximal g closely tracks the ridge of maximal finite-horizon success probability Psuccess(T), and a simple T→∞ consistency check shows convergence of argmaxκ Psuccess(T) → argmaxκ g(γ,κ).