# Remarks on Entropy Formulae for Linear Heat Equation

## TL;DR

This paper introduces new entropy formulas for the linear heat equation on Riemannian manifolds with nonnegative Ricci curvature, extending concepts from Ricci flow to static manifolds.

## Contribution

It develops novel entropy formulas for the linear heat equation on static manifolds, inspired by Ricci flow entropy concepts.

## Key findings

- Established new entropy formulas for the linear heat equation.
- Extended Ricci flow entropy ideas to static Riemannian manifolds.
- Provided mathematical analogies to Ricci flow entropy results.

## Abstract

In this note, we prove some new entropy formula for linear heat equation on static Riemannian manifold with nonnegative Ricci curvature. The results are analogies of Cao and Hamilton's entropies for Ricci flow coupled with heat-type equations.