Absence of classical and quantum mixing

TL;DR

This paper demonstrates that classical degrees of freedom coupled to quantum ones do not acquire quantum fluctuations, and with additional assumptions, only purely classical or quantum dynamics are possible.

Contribution

It establishes conditions under which classical and quantum systems remain distinct, preventing hybrid quantum-classical fluctuations or mixed dynamics.

Findings

Classical degrees of freedom do not inherit quantum fluctuations when coupled.

Imposing a canonical structure restricts dynamics to purely classical or quantum.

Hybrid classical-quantum dynamics are ruled out under the given assumptions.

Abstract

It is shown, under mild assumptions, that classical degrees of freedom dynamically coupled to quantum ones do not inherit their quantum fluctuations. It is further shown that, if the assumptions are strengthen by imposing the existence of a canonical structure, only purely classical or purely quantum dynamics are allowed.