Classicality and connectedness for state property systems and closure spaces

TL;DR

This paper leverages the categorical equivalence between state property systems and closure spaces to develop a decomposition theorem, enabling the splitting of systems into classical and nonclassical components.

Contribution

It introduces a novel decomposition theorem for state property systems based on connectedness in closure spaces, enhancing understanding of their classical and nonclassical parts.

Findings

Decomposition of state property systems into classical and nonclassical parts

Use of connectedness in closure spaces for system analysis

Categorical equivalence facilitates the decomposition approach

Abstract

It has been shown that there is a categorical equivalence between the category SPS of state property systems and the category Cl of closure spaces. In this note we prove, using this equivalence between categories, that the concept of connectedness for closure spaces can be used to formulate a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'.