Axiomatic tests for the Boltzmann distribution

Abstract The Boltzmann distribution family describes a single parameter (temperature) class of probability distributions over state space; at any given temperature, the ratio probabilities two states depends exponentially on their difference in energy. Beyond physics, this is very popular many important disciplines, under different names with interpretations. Such widespread use diverse fields suggests common conceptual structure. We identify such structure basis few natural axioms that can be statistically tested. Our axiomatic characterization thus provides alternative empirical tests Boltzmannian modeling theories.