Cutoff beyond non-negative curvature

We study how a relaxed gradient estimate is enough to prove cutoff for several new families of Markov processes, within the varentropy framework of [Sal25]. In particular, we show how certain regularization estimates from hypocoercivity theory allow one to prove cutoff for kinetic dynamics. Moreover, we prove cutoff for some families of diffusions with non-convex potentials and for mean-field dynamics, as well as for biased random walks on the symmetric group, giving a simple proof of a far-reaching extension of a result of [NY24].