We study the entropy production of the sandwiched R\'enyi divergence under a primitive Lindblad equation with GNS-detailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched R\'enyi divergence for any order $\alpha\in (0,\infty)$. This extends a previous result by Carlen and Maas [Journal of Functional Analysis, 273(5), 1810--1869] for the quantum relative entropy (i.e., $\alpha=1$). Moreover, we show that the sandwiched R\'enyi divergence with order $\alpha\in (0,\infty)$ decays exponentially fast under the time-evolution of such a Lindblad equation. 查看全文>>