Blind Thermodynamic Ontology Discovery from Anonymous Experiments

2026-09-20

AI Summary

本文提出了一种从匿名实验中发现隐藏热力学本体的方法，通过可操作的识别理论和多项式时间算法来提取并验证物理量。

Abstract

Before a machine learning model can learn a thermodynamic equation of state, it must discover what its measurements represent: which channels scale with system size, which are intensive conjugates, how sectors pair through contact, and which potential governs stability. When sensors expose only an unknown linear mixture of extensive states and intensive responses, passive observations cannot disentangle physical quantities from coordinate artifacts. We formulate the problem of discovering this hidden thermodynamic ontology directly from anonymous controlled experiments. We present an operational identifiability theory and a constructive polynomial-time algorithm that extracts extensive and intensive scaling sectors from replication contrasts, recovers their dual cotangent pairing from thermal contact and reciprocity, verifies a globally admissible concave potential via discrete cyclic concavity, and determines an invariant matroid of reservoir ensembles. We prove that the residual observational equivalence is strictly (x, lambda) ~ (A x, a A^{-T} lambda + beta), establishing the sharp observational limit that no permitted experiment can break. Blind evaluations on van der Waals fluids and Curie-Weiss magnets confirm robust recovery under ill-conditioned mixing, correctly resolving anonymous Maxwell tie-lines while rejecting non-equilibrium continuations. External validation across six real fluids from the NIST WebBook demonstrates that operational ontology discovery transfers across real physical substances without coordinate leakage.

Problem

• thermodynamic ontology
• anonymous experiments
• extensive and intensive scaling
• thermal contact
• concave potential

Innovation

• operational identifiability theory
• constructive polynomial-time algorithm
• extensive and intensive scaling sectors
• discrete cyclic concavity
• invariant matroid