# DAN

## Seminar

### Convex decay of entropy in interacting systems

Seminar Room 1, Newton Institute

#### Abstract

For a Markov process, the exponential decay of relative entropy with respect to the invariant measure corresponds to a functional inequality sometimes called "Modified logarithmic Sobolev inequality" (MLSI). We consider a stronger inequality, that, besides exponential decay, implies that the relative entropy is convex in time. The advantage of this inequality is that it can be obtained, for some systems of interacting particle, via a Bakry-Emery-type approach, avoiding more complicated martingale methods. After having illustrated this approach, I will present some recent progresses on the subject, obtained in collaboration with G. Posta.#### Video

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