Transition operators assigned to physical systems

TL;DR

This paper introduces a method to assign transition operators to physical systems based on their state transition relations, enabling the recovery of these relations from the operators under certain conditions.

Contribution

It formalizes the assignment of transition operators to physical systems and identifies conditions for reconstructing the transition relation from these operators.

Findings

Defined a framework linking transition relations to operators

Established conditions for relation recovery from operators

Provided a mathematical foundation for analyzing physical system dynamics

Abstract

By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on the set of states describing this transition. Our aim is to assign to every such system an operator on the set of propositions which is fully determined by the mentioned relation. We establish conditions under which the given relation can be recovered by means of this transition operator.