Axiomatic Tests for the Boltzmann Distribution
Probability
2020-07-01 v2
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.
Cite
@article{arxiv.2006.15970,
title = {Axiomatic Tests for the Boltzmann Distribution},
author = {Simone Cerreia-Vioglio and Fabio Maccheroni and Massimo Marinacci and Aldo Rustichini},
journal= {arXiv preprint arXiv:2006.15970},
year = {2020}
}