The Weitzenbock formula on the Wiener space and its application to the asymptotic estimate of entropy

TL;DR

This paper applies the Weitzenbock formula to the Wiener space to derive explicit estimates on the entropy's time derivative for solutions of the Fokker-Planck equation, advancing understanding of entropy behavior in stochastic analysis.

Contribution

It introduces a novel application of the Weitzenbock formula on Wiener space to estimate entropy evolution in the Fokker-Planck equation.

Findings

Derived explicit bounds on entropy derivative over time

Connected geometric analysis with stochastic PDEs

Enhanced understanding of entropy asymptotics in Wiener space

Abstract

We consider the Fokker-Planck equation on the abstract Wiener space associated to the Ornstein-Uhlenbeck operator. Using the Weitzenb\"ock formula, we prove an explicit estimate on the time derivative of the entropy of the solution to the Fokker-Planck equation.