Consistent classical and quantum mixed dynamics

TL;DR

This paper introduces a consistent mixed classical-quantum dynamics framework that satisfies algebraic and separability requirements, providing a physically complete model with generalized Ehrenfest relations and thermodynamic consistency.

Contribution

It proposes a novel mixed dynamics model that meets minimal algebraic and separability criteria, advancing the theoretical foundation of classical-quantum interactions.

Findings

Satisfies Salcedo's algebraic requirements for mixed dynamics

Derives generalized Ehrenfest relations for observables

Defines thermodynamic mixtures consistent with classical ensembles

Abstract

A recent proposal for mixed dynamics of classical and quantum ensembles is shown, in contrast to other proposals, to satisfy the minimal algebraic requirements proposed by Salcedo for any consistent formulation of such dynamics. Generalised Ehrenfest relations for the expectation values of classical and quantum observables are also obtained. It is further shown that additional desirable requirements, related to separability, may be satisfied under the assumption that only the configuration of the classical component is directly accessible to measurement, eg, via a classical pointer. Although the mixed dynamics is formulated in terms of ensembles on configuration space, thermodynamic mixtures of such ensembles may be defined which are equivalent to canonical phase space ensembles on the classical sector. Hence, the formulation appears to be both consistent and physically complete.