Herbst's argument: an entropy bound $\mathrm{Ent}(e^{sf})\le c s^2\,\mathbb{E}e^{sf}$ for all $s>0$ implies $\mathbb{E}e^{sf}\le e^{s\mathbb{E}f+cs^2}$

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Herbst's argument: an entropy bound $\mathrm{Ent}(e^{sf})\le c s^2\,\mathbb{E}e^{sf}$ for all $s>0$ implies $\mathbb{E}e^{sf}\le e^{s\mathbb{E}f+cs^2}$ · Prove2Me