  This note presents a method based on Feynman-Kac semigroups for logarithmic
Sobolev inequalities. It follows the recent work of Bonnefont and Joulin on
intertwining relations for diffusion operators, formerly used for spectral gap
inequalities, and related to perturbation techniques. In particular, it goes
beyond the Bakry-{\'E}mery criterion and allows to investigate high-dimensional
effects on the optimal logarithmic Sobolev constant.The method is illustrated
on particular examples (namely Subbotin distributions and double-well
potentials), for which explicit dimension-free bounds on the latter constant
are provided. We eventually discuss a brief comparison with the Holley-Stroock
approach.
