A Bayesian interpretation of abrupt phase transitions

TL;DR

This paper reviews the thermodynamics of abrupt phase transitions through a Bayesian lens, showing how key concepts like transition temperature and latent heat relate to inference problems with yes/no questions and expectation data.

Contribution

It introduces a Bayesian interpretation of first-order phase transitions, connecting thermodynamic concepts to inference theory and maximum entropy principles.

Findings

Transition temperature and latent heat have equivalents in inference problems.

Thermodynamic concepts can be understood through maximum entropy inference.

The formalism unifies phase transition analysis with Bayesian inference.

Abstract

The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat and entropy difference between phases will inevitably have an equivalent in any problem of inferring the result of a yes/no question, given information in the form of expectation values.