Global Observables in Statistical Mechanics

Abstract

Abstract We present 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 $$C^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -algebraic setting, without relying on any specific representation.