Axiomatic tests for the Boltzmann distribution. Issue 1 (31st January 2021)

• Record Type: Journal Article
• Authors: Cerreia-Vioglio, Simone; Maccheroni, Fabio; Marinacci, Massimo; Rustichini, Aldo
• Is Part Of: Journal of statistical mechanics. Issue 1(2021)
• Publication Date: 2021-01-31
• Subjects: game theory -- mathematical economics -- general equilibrium models; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/abd4ce
• Languages: English
• ISSNs: 1742-5468

Abstract

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