Logarithmic Sobolev inequalities

Log-Sobolev inequalities are a happy medium between classical “higher-order” Sobolev inequalities attached to generators of Markovian semigroups and the corresponding Poincaré inequalities; the former is not robust and the latter is too weak. In this talk, we’ll make at least half of this precise and discuss log-Sobolev inequalities in the specific context of the Bakry-Emery theory. This context has the upshot of being heavily involved with the discussion of entropy production and energy forms, which is crucial in statistical mechanics of large systems; we’ll also discuss this to show why the relative entropy is such a great topology.