Melchior Wirth, Institute of Science and Technology Austria
Some recent progress on (modified) logarithmic Sobolev inequalities for quantum Markov semigroups that act on infinite-dimensional von Neumann algebras and are not necessarily symmetric with respect to a trace will be presented. I will discuss a de Bruijn identity in this setting, which implies the equivalence of the modified logarithmic Sobolev inequality and exponential entropy decay. For GNS-symmetric semigroups I will give an intertwining criterion for the modified logarithmic Sobolev inequality and show that the logarithmic Sobolev inequality and hypercontractivity are equivalent. This talk is based on joint work with Martijn Caspers, Matthijs Vernooij and Haonan Zhang.