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).