The computational challenges posed by many-particle quantum systems are often overcome by mixed quantum-classical (MQC) models in which certain degrees of freedom are treated as classical while others are retained as quantum. One of the fundamental questions raised by this hybrid picture involves the characterization of the information associated to MQC systems. Based on the theory of dynamical invariants in Hamiltonian systems, here we propose a family of hybrid entropy functionals that consistently specialize to the usual R\'enyi and Shannon entropies. Upon considering the MQC Ehrenfest model for the dynamics of quantum and classical probabilities, we apply the hybrid Shannon entropy to characterize equilibrium configurations for simple Hamiltonians. The present construction also applies beyond Ehrenfest dynamics.

翻译：多粒子量子系统带来的计算挑战通常通过混合量子-经典模型得以克服，该模型将某些自由度处理为经典自由度，而将其他自由度保留为量子自由度。这种混合图景引发的一个基本问题涉及混合量子-经典系统相关信息的表征。基于哈密顿系统中动力学不变量的理论，本文提出了一族混合熵泛函，它们能一致地特化为通常的Rényi熵与香农熵。通过考虑量子与经典概率动力学的混合量子-经典Ehrenfest模型，我们应用混合香农熵来刻画简单哈密顿量的平衡构型。本构建方法同样适用于Ehrenfest动力学之外的情形。