Phi-entropy inequalities and Fokker-Planck equations

TL;DR

This paper introduces new Phi-entropy inequalities for diffusion semigroups that include the Gaussian isoperimetric function, with applications to analyzing the long-term behavior of Fokker-Planck equation solutions.

Contribution

It provides novel Phi-entropy inequalities under curvature-dimension conditions, extending understanding of diffusion semigroups and their long-term dynamics.

Findings

Derived new Phi-entropy inequalities including Gaussian isoperimetric function

Applied inequalities to study long-time behavior of Fokker-Planck solutions

Enhanced theoretical framework for diffusion semigroup analysis

Abstract

We present new $\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.