The introduction of symmetry constraints within MaxEnt Jaynes's methodology

TL;DR

This paper enhances Jaynes's MaxEnt method by integrating symmetry constraints through a generalized geometric probability framework, enabling the inclusion of group theory in probabilistic physical theories.

Contribution

It introduces a novel framework that incorporates symmetry constraints into MaxEnt, extending its applicability to generalized probabilistic theories.

Findings

Framework successfully integrates symmetry constraints into MaxEnt.

Examples demonstrate the practical application of the method.

Enhanced MaxEnt approach broadens its theoretical scope.

Abstract

We provide a generalization of the approach to geometric probability advanced by the great mathematician Gian Carlo Rota, in order to apply it to generalized probabilistic physical theories. In particular, we use this generalization to provide an improvement of the Jaynes' MaxEnt method. The improvement consists in providing a framework for the introduction of symmetry constrains. This allows us to include group theory within MaxEnt. Some examples are provided.