Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum dynamical semigroup, we find a decomposition of the infinitesimal generator of the dynamics, that allows to relate the von Neumann entropy rate with the divergence-based quantum Fisher information, at any time. Applied to quantum Gaussian channels that are dynamical semigroups, our decomposition leads to the quantum analog of the generalized classical de Bruijn identity, thus expressing the quantum fluctuation-dissipation relation in that kind of channels. Finally, from this perspective, we analyze how stationarity arises.

翻译：开放量子系统的Von Neumann entropy 速率,一般是用恒温动力学的第二定律,包括恒温动力学的倍增率和环流速率写成的。当开放量子系统进化与量子动态半组相对应时,我们发现该动态的无限微量生成器的分解,它能够在任何时候将冯Neumann 的增量率与基于差异的量子飞航信息联系起来。我们应用到有动态半组的量子高斯频道,我们的分解导致形成典型德布鲁琴特征的量子类相似,从而表达出这种渠道的量子波动-分散关系。最后,我们从这个角度分析如何产生定态性。