Maximum information entropy principle and the interpretation of probabilities in statistical mechanics - a short review

TL;DR

This paper explores an alternative to traditional statistical mechanics using the maximum information entropy principle (MaxEnt), showing its logical extension of Gibbs formalism and its interpretation of probabilities independent of frequency-based views.

Contribution

It demonstrates that MaxEnt provides a frequency-independent interpretation of probabilities in statistical mechanics, aligning with the Gibbs method and the law of large numbers.

Findings

MaxEnt formalism extends Gibbs ensemble theory.

Probabilities in statistical mechanics can be interpreted via MaxEnt independently of frequency.

Relative frequencies match MaxEnt probabilities in large ensembles.

Abstract

In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt formalism is the logical extension of the Gibbs formalism of equilibrium statistical mechanics that is entirely independent of the frequentist interpretation of probabilities only as factual (i.e. experimentally verifiable) properties of the real world. Furthermore, we show that, consistently with the law of large numbers, the relative frequencies of the ensemble of systems prepared under identical conditions (i.e. identical constraints) actually correspond to the MaxEnt probabilites in the limit of a large number of systems in the ensemble. This result implies that the probabilities in statistical mechanics can be interpreted, independently of the frequency interpretation, on the basis of the maximum information entropy principle.