The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics

TL;DR

This paper explores the geometric and convex properties of quantum Gibbs families at ultra-cold temperatures, extending maximum-entropy inference and irreducible correlation concepts to absolute zero.

Contribution

It introduces a novel extension of the MaxEnt framework and irreducible correlation to zero temperature, addressing discontinuities in quantum Gibbs families.

Findings

Extended MaxEnt representation to zero temperature

Analyzed convex geometry of quantum Gibbs families

Identified discontinuities in the norm closure of Gibbs families

Abstract

We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.