# Optimal Transportation to the Entropy-Power Inequality

## TL;DR

This paper introduces a straightforward optimal transportation-based proof of the entropy-power inequality, also deriving a reverse inequality and generalizations, applicable in multiple dimensions.

## Contribution

It provides a novel, simple proof of the entropy-power inequality using optimal transportation, including a reverse form and generalizations across dimensions.

## Key findings

- Proof of the entropy-power inequality via optimal transportation
- Derivation of a reverse inequality involving conditional entropy
- Extension of the method to multiple dimensions

## Abstract

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential entropy which has its own interest. It can also be generalized in various ways. The equality case is easily captured by this method and the proof is formally identical in one and several dimensions.