从匿名实验中盲发现热力学本体：一项可识别性理论与多项式时间算法

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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.

Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:	arXiv:2609.23387 [cs.LG]
	(or arXiv:2609.23387v2 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2609.23387 arXiv-issued DOI via DataCite

Submission history

From: Linzhe Zhang [view email]
[v1] Sun, 20 Sep 2026 06:11:40 UTC (343 KB)
[v2] Thu, 29 Oct 2026 10:32:33 UTC (343 KB)