What is "system" : the arguments from the decoherence theory

TL;DR

This paper explores how the separability of the interaction Hamiltonian in decoherence theory can serve as a criterion for defining 'system' and 'environment', emphasizing their interconnectedness and mutual dependence.

Contribution

It demonstrates that defining 'system' via Hamiltonian separability is inherently linked to the environment, extending this idea to interacting systems and providing a simple illustrative example.

Findings

Separable Hamiltonian conditions relate to system-environment definitions

System and environment are mutually dependent in their definitions

The approach offers an inverse perspective to traditional decoherence analysis

Abstract

Within the decoherence theory we investigate the physical background of the condition of the separability (diagonalizability in noncorrelated basis) of the interaction Hamiltonian of the composite system, "system plus environment". It proves that the condition of the separability may serve as a criterion for defining "system", but so that "system" cannot be defined unless it is simultaneously defined with its "environment". When extended to a set of the mutually interacting composite systems, this result implies that the separability conditions of the local interactions are mutually tied. The task of defining "system" (and "environment") via investigating the separability of the Hamiltonian is a sort of the inverse task of the decoherence theory. A simple example of doing the task is given.