Generalized entropic structures and non-generality of Jaynes' Formalism

TL;DR

This paper examines the limitations of Jaynes' Formalism in deriving probability distributions, showing it is only valid for certain entropy definitions and highlighting the need for generalized entropic structures.

Contribution

The study analyzes inconsistencies in Jaynes' Formalism and demonstrates its validity only for specific entropy definitions, proposing a broader framework.

Findings

Jaynes' Formalism is valid only for specific entropy types.

Inconsistencies arise when applying Jaynes' Formalism to generalized entropies.

A generalized framework is necessary for consistent distribution derivation.

Abstract

The extremization of an appropriate entropic functional may yield to the probability distribution functions maximizing the respective entropic structure. This procedure is known in Statistical Mechanics and Information Theory as Jaynes' Formalism and has been up to now a standard methodology for deriving the aforementioned distributions. However, the results of this formalism do not always coincide with the ones obtained following different approaches. In this study we analyse these inconsistencies in detail and demonstrate that Jaynes' formalism leads to correct results only for specific entropy definitions.