通过大偏差理论从观测约束中推断微观解释结构
Inferring Microscopic Explanatory Structures from Observational Constraints via Large Deviations
AI总结：
本文通过大偏差理论从观测约束中推断微观结构，展示在无先验假设下如何从无序数据中推断出有序结构。
摘要：
我们研究了宏观观测约束如何限制可接受的微观解释结构，当不假设任何内在秩序或动态时。从无序的测量结果集合出发，我们将推断 formulation 为一个受约束的大偏差问题，选择最小化与参考测度相对熵的概率分配。我们展示，在所有与给定宏观约束兼容的微观结构中，那些使观察在统计上最典型的结构被选择。作为明确的例子，我们展示了如何在约束下纯从推断中出现有序的微观结构，即使参考测度完全对称。秩序因此不是假设而是推断，这里仅作为更广泛类别的关系解释假说受观察约束的示例。
英文摘要：
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.
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