This work formalizes the Effective Theory of Information-Based Instrumentation (IBI), a precision engineering framework that redefines matter characterization through the integration of information physics and state estimation. IBI shifts the focus from passive measurement toward an active observation model, optimizing data extraction in complex ionic systems within a quantified domain of validity. By applying an interaction Hamiltonian and the Mori-Zwanzig projection formalism, a temporal response kernel χ(t − t′) is derived, allowing the separation of the coherent signal from the system's memory. This physical foundation feeds a Physics-Informed Kalman Filter with Augmented States (3 states), designed to operate on low-power microcontrollers. The mathematical architecture is grounded in Information Geometry, using the Fisher matrix to maximize distinguishability between analytes and define resolution limits under the Cramér-Rao Bound. The work introduces the Index of Metrological Efficiency (ηIBI ) as a universal metric to evaluate energy cost versus informational gain. Robust numerical validation (100 Monte Carlo runs, seed=42) reveals that EKF and LKF produce identical results (R2 = 0,917 ± 0,013 in normal phase, R2 = 0,763 ± 0,025 under interference, ∆R2 = 0,154) due to the model's linearity. AKF (α = 0,1) demonstrated optimal performance with R2 = 0,938±0,010 (normal phase) and R2 = 0,898±0,013 (interference), with ∆R2 = 0,040 (74 % more resilient than LKF/EKF) and variance reduction of 13,5×. UKF showed R2 = 0,918 ± 0,013 (pre) and R2 = 0,769 ± 0,025 (post). Analysis of the Einstein-Informational Bridge shows a DKL reduction of 0,199 nats (11.5 %) for EKF/LKF y 0,178 nats for UKF, with geodesic distances on the order of 10E−7, validating filter convergence as a trajectory on the Fisher manifold. The system is completely observable for this specific configuration (rank=3/3, condition number=2913.61). As an effective theory, IBI explicitly recognizes its limits of applicability (ionic strength < 0,1 M, linear regime, temperatures 273 - 353 K).
Zamora et al. (Mon,) studied this question.