Information-Rate Bounds on Inductive Energy Harvesting from Magnetoconvective Thermal Fluctuations in a Hexagonal Prism Cell

We propose and analyze a physically auditable protocol for converting near-equilibrium thermalfluctuations in a conducting fluid into electrical power delivered to an external load by inductivemagnetohydrodynamic (MHD) transduction, with continuous two-point thermometry performed bya qubit-based sensor of finite efficiency. The central result is an information-thermodynamic inequal-ity constraining the net extracted power Pout (electrical load power minus externally supplied con-trol/actuation power, with Joule/viscous losses consistently accounted) by the mutual-informationrate ˙I entering the feedback loop:˙Σ = ˙I − βPout ≥ 0 ⇒ Pout ≤ kBT ˙I, (1)where β ≡ 1/(kBT ) and ˙Σ is total entropy production rate. To connect (1) to measurable pa-rameters, we derive a reduced stochastic model valid near the onset of magnetoconvection: a slowend-to-end temperature-gradient mode g(t) coupled to a convective roll amplitude A(t) governed bya noisy Landau–Stuart equation with magnetic stabilization through the Chandrasekhar number.Continuous qubit thermometry provides a scalar observation channel for g(t) with efficiency η; themutual-information rate ˙I is expressed in estimation-theoretic form (Duncan identity) and com-puted from the steady-state error covariance of the associated Kalman–Bucy filter (matrix Riccati).We further derive an explicit induction-to-load reduction in quasi-static MHD: the electromotiveforce and delivered load power are linear-quadratic functionals of A(t) with geometry determinedby a harmonic weight function solving the Laplace conduction problem with electrode boundaryconditions. The framework yields falsifiable scaling predictions for Pout(η) and an “entropy audit”variable ˙Σaudit = ˙I − βPout that must remain nonnegative if the accounting and coarse-graining arecorrect. We emphasize that this does not violate the second law of thermodynamics: the boundPout ≤ kB T I constrains extractable power by available measurement resources, and net poweraccounts for all control and measurement costs.