The log-Sobolev inequality (LSI) is a very useful tool for analyzing high-dimensional situations. For example, the LSI can be used for deriving hydrodynamic limits, for estimating the error in stochastic homogenization, for deducing upper bounds on the mixing times of Markov chains, and even in the proof of the Poincare conjecture by Perelman. For most applications, it is crucial that the...