Global observables in statistical mechanics

TL;DR

This paper introduces a unified $C^*$-algebraic framework for constructing global observables in statistical mechanics, applicable to both commutative and non-commutative cases, without depending on specific representations.

Contribution

It provides a novel, unified method for defining global observables directly within the $C^*$-algebraic setting, advancing the theoretical foundation of statistical mechanics.

Findings

Unified construction of global observables in $C^*$-algebras

Applicable to both commutative and non-commutative cases

Framework does not rely on specific representations

Abstract

This note presents a canonical construction of global observables -- sometimes referred to in the literature as macroscopic observables or observables at infinity -- in statistical mechanics, providing a unified treatment of both commutative and non-commutative cases. Unlike standard approaches, the framework is formulated directly in the $C^*$-algebraic setting, without relying on any specific representation.