Math @ Duke

Publications [#343501] of Yu Cao
Papers Published
 Cao, Y; Lu, J; Lu, Y, Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNSdetailed balance,
Journal of Mathematical Physics, vol. 60 no. 5
(May, 2019),
pp. 052202052202, AIP Publishing [doi]
(last updated on 2019/07/22)
Abstract: © 2019 Author(s). We study the entropy production of the sandwiched Rényi divergence under the primitive Lindblad equation with Gel'fandNaimarkSegaldetailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched Rényi divergence of any order α ∈ (0, ∞). This extends a previous result by Carlen and Maas [J. Funct. Anal. 273(5), 18101869 (2017)] for the quantum relative entropy (i.e., α = 1). Moreover, we show that the sandwiched Rényi divergence of any order α ∈ (0, ∞) decays exponentially fast under the time evolution of such a Lindblad equation.


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