An algebraic theory of infinite classical lattices III: Theory of single measurements

TL;DR

This paper develops an algebraic framework for understanding single measurements on infinite classical lattices, focusing on the probabilistic outcomes when a finite system interacts with an infinite heat bath.

Contribution

It introduces a theoretical model for single measurements on infinite lattices, incorporating the effects of the surrounding heat bath and stationary distributions.

Findings

Characterizes the source of randomness in measurements.

Describes the probability distribution of measurement outcomes.

Provides a formalism for states and measurement in infinite lattices.

Abstract

This is the third in a series of papers dealing with the algebraic theory of infinite classical lattices. This paper presents a theory of single measurements on a lattice which we represent as comprising a finite subvolume--the system of measurement--immersed in an infinite surround or ``heat bath'' which determines the system's state. We consider the class of all stationary distributions on the set of microcanonical states of the infinite lattice. The theory addresses the question, ``For a lattice initially in state A, say, what is the probability that measurement of a certain quantity will take a value in (a,b)?'' Discussion includes description of the source of randomness in a measurement as well as characterization of the given states A.