Inferring Microscopic Explanatory Structures from Observational Constraints via Large Deviations

TL;DR

This paper presents a method to infer microscopic structures consistent with macroscopic observational constraints using large deviation principles, highlighting how order can emerge purely from inference without prior assumptions.

Contribution

It introduces a framework for deriving microscopic explanations from macroscopic data via constrained large deviations, emphasizing the emergence of order without prior assumptions.

Findings

Ordered microscopic structures can emerge from inference under constraints.

The method selects the most statistically typical structures compatible with observations.

Order can be inferred solely from observational constraints without assuming intrinsic order.

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.