论文标题
量子马尔可夫半群的完整梯度估计
Complete gradient estimates of quantum Markov semigroups
论文作者
论文摘要
在本文中，我们介绍了配备有正常忠实的奇特状态的冯·诺伊曼代数对称对称量子马尔可夫半群的完整梯度估计，这意味着熵的半跨性别性相对于最近引入的非交换性的2-Wasserstein距离。我们表明，在张量产品和免费产品下，这种完整的梯度估计值稳定，并为许多示例确定其有效性。作为应用程序，我们证明了完全修改的对数Sobolev不等式，对于自由组因子的泊松型半群，最佳常数。
In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.
