# Phase Transitions as the Breakdown of Statistical Indistinguishability

arXiv: https://arxiv.org/abs/2604.15773 · HTML: https://mlsanity.com/paper/2604.15773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 8 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Abstract (arXiv)

We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This perspective provides a general, order-parameter-free framework that does not rely on model-specific insights or learning procedures. We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework. As a concrete realization, we employ a distribution-free two-sample run test and demonstrate that the critical point of the two-dimensional Ising model is accurately identified without prior knowledge of the order parameter.