Phase Transitions as the Breakdown of Statistical Indistinguishability

• URL: http://arxiv.org/abs/2604.15773v1
• Date: Fri, 17 Apr 2026 07:29:07 GMT
• Title: Phase Transitions as the Breakdown of Statistical Indistinguishability
• Abstract summary: We introduce a novel characterization of phase transitions based on hypothesis testing.<n>We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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