Under LSI and convexity assumptions on the target, the relative entropy of underdamped Langevin dynamics decays at an explicit rate proportional to sqrt(ρ) with constant depending on a scaled friction parameter.
Brenier,Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics44(1991), 375–417
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A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
Under LSI and convexity assumptions on the target, the relative entropy of underdamped Langevin dynamics decays at an explicit rate proportional to sqrt(ρ) with constant depending on a scaled friction parameter.