Data Set Models and Exponential Families in Statistical Physics and Beyond

TL;DR

This paper generalizes the exponential family framework beyond probability theory, applying it to classical and quantum statistical physics, and predicts novel applications such as modeling quantum states in phase space.

Contribution

It introduces a broad, probability-free formalism for exponential families, unifying classical and quantum models within a geometric framework.

Findings

Exponential families are valid beyond probability theory.

Classical and quantum statistical models fit into the new formalism.

Quantum states can be represented as points in classical phase space.

Abstract

The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical statistical physics fit into the new formalism. Other less obvious applications are predicted. For instance, quantum states can be modeled as points in a classical phase space and the resulting model belongs to the exponential family.