TITLE:
Information-Theoretic Criterion for Physical Model Selection: Mathematical Foundations and Independent Experimental Tests
AUTHORS:
Boris Menin
KEYWORDS:
Finite Information Quantity (FIQ), Physical Model Selection, Information Theory, Comparative Uncertainty, Model Information Content, Maximum Entropy, Measurement Uncertainty, Experimental Verification
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.11,
November
10,
2026
ABSTRACT: When constructing a physical model, the researcher inevitably limits the number of quantities used to describe the phenomenon under study. This paper develops the Finite Information Quantity (FIQ) approach, which allows for the quantitative assessment of the information limitation arising from such a choice. A physical model is considered a finite representation of the system under study, the information content of which is determined by the set of physical quantities used. Based on this, an expression for comparative uncertainty is derived and the value of εopt is determined. This value is calculated directly from the information structure of the model before the experiment and without using measurement results. The equiprobability of informationally indistinguishable FIQs is justified by the principle of maximum entropy; the invariance of the criterion under changes in units of measurement and informationally equivalent representations of the model is also examined. For experimental verification, a procedure is proposed for independently determining experimental comparative uncertainty εexp from published data and comparing it with εopt without adjusting FIQ parameters. The method was applied to measurements of liquid zirconium density, heat transfer in a bulk layer, and two independent measurements of the gravitational constant. The resulting εexp/εopt ratios were ≈2.92 for zirconium density and ≈4.44 and 4.43 for the two gravitational-constant measurements. Analysis of the heat transfer data revealed the need to independently determine the experimental uncertainty and the range of possible values of the measured quantity. The results demonstrate that the FIQ defines a priori computable benchmark for the information content of a physical model, comparable with the achieved experimental uncertainty without adjusting FIQ parameters. εopt is treated as a descriptive balance benchmark, not as a lower bound.