🤖 AI Summary
This study addresses the challenge of inferring plausible microscopic explanations solely from macroscopic observational constraints, without relying on prior assumptions about microstructure or dynamics. The problem is formulated as a constrained large deviations optimization: among all microscopic configurations compatible with the given macroscopic constraints, the statistically most typical solution is selected by minimizing the relative entropy with respect to a symmetric reference measure uniquely determined by the measurement setup. Remarkably, this approach requires no predefined notion of order yet spontaneously yields structured interpretations—such as ordered relationships—as emergent properties. The work demonstrates that even under a fully permutation-symmetric reference measure, ordered microscopic structures can naturally arise as typicality-optimal solutions.
📝 Abstract
We study how macroscopic observational constraints restrict admissible microscopic explanatory structures when no intrinsic order or dynamics is assumed a priori. Starting from an unordered collection of measurement outcomes, we formulate inference as a constrained large deviation problem, selecting probability assignments that minimize relative entropy with respect to a reference measure determined solely by the measurement setup. We show that among all microscopic structures compatible with a given macroscopic constraint, those rendering the observation statistically most typical are selected. As an explicit illustration, we demonstrate how ordered microscopic structures can emerge purely from inference under constraint, even when the reference measure is fully permutation symmetric. Order is thus not assumed but inferred, serving here only as an illustrative example of a broader class of relational explanatory hypotheses constrained by observation.