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.

Axiomatic tests for the Boltzmann distribution

Simone Cerreia-Vioglio;Fabio Maccheroni
;
Massimo Marinacci;
2021

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.
2021
CERREIA VIOGLIO, Simone; Maccheroni, FABIO ANGELO; Marinacci, Massimo; Rustichini, Aldo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/4034627
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