Fluctuation and dissipation in memoryless open quantum evolutions

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