Effect algebras and statistical physical theories

Abstract

The dichotomic physical quantities of a physical system can be naturally hosted in a mathematical structure, called effect algebra, of which orthomodular posets and Boolean algebras are particular examples. We examine how effect algebras arise inside statistical physical theories and, conversely, we study to what extent an effect algebra can be taken as a primitive structure on which a satisfactory statistical physical model equipped with a convex set of states can be constructed.