# Blind Thermodynamic Ontology Discovery from Anonymous Experiments

arXiv: https://arxiv.org/abs/2609.23387 · HTML: https://mlsanity.com/paper/2609.23387/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Score-based Causal Representation Learning: Linear and General Transformations](https://mlsanity.com/paper/2402.00849/) (2024)
- [Thermodynamically consistent machine learning model for excess Gibbs energy](https://mlsanity.com/paper/2509.06484/) (2025)
- [Differentiable Thermodynamic Phase-Equilibria for Machine Learning](https://mlsanity.com/paper/2603.11249/) (2026)

## Built on by (most cited first, 1 of 1)

- [Certified Task-Conditioned Active Observability](https://mlsanity.com/paper/2609.28520/) (2026)

## Abstract (arXiv)

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.