Axiomatic Tests for the Boltzmann Distribution

TL;DR

This paper provides an axiomatic characterization of the Boltzmann distribution, enabling simple empirical tests for models across various disciplines that assume this distribution.

Contribution

It introduces a set of natural axioms that uniquely characterize the Boltzmann distribution, facilitating empirical validation of related models.

Findings

Axioms uniquely identify the Boltzmann distribution

Empirical tests based on axioms are straightforward

Applicable across diverse fields like economics and psychology

Abstract

The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same family is known in other disciplines (economics, psychology, computer science) with different names and interpretations. Such widespread use in very diverse fields suggests a common conceptual structure. We identify it on the basis of few natural axioms. Checking whether observables satisfy these axioms is easy, so our characterization provides a simple empirical test of the Boltzmannian modeling theories.