Quantum Markov semigroups models the time evolution of dissipative open quantum systems. They are noncommutative version of Markov semigroups where the underlying function space is replaced by matrix or operator algebras. For a Markov semigroup, the modified logarithmic Sobolev inequality (MLSI) describes the convergence property in terms of relative entropy. It was a famous result by Bakry and Emery that the heat semigroup on a compact Riemannian manifold satisfies MLSI if the Ricci curvature admits a strictly positive lower bound. Recently Carlen and Maas introduce the notation of Ricci curvature lower bound for quantum Markov semigroups and show that a positive Ricci lower bound implies MLSI in the noncommutative setting. In this talk, I will present an approach to MLSI via Ricci curvature bounded below but not necessarily positive. We show that ``central'' semigroups on groups and quantum groups admits nonnegative curvature and MLSI. This approach gives new examples of MLSI in both operator algebras and quantum information theory. This talk is based on joint work with Michael Brannan and Marius Junge.