Axiomatic tests for the Boltzmann distribution

Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number013406
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2021
Issue number1
DOIs
StatePublished - Jan 2021

Bibliographical note

Publisher Copyright:
© 2021 IOP Publishing Ltd and SISSA Medialab srl

Keywords

  • Game theory
  • General equilibrium models
  • Mathematical economics

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