# Two remarks on generalized entropy power inequalities

## TL;DR

This paper explores generalized entropy power inequalities by providing a counter-example to monotonicity and entropy comparison, and introduces a complex analogue of a recent dependent inequality with a simplified proof.

## Contribution

It constructs a counter-example to monotonicity in generalized entropy power inequalities and presents a simple proof for a complex analogue of a recent dependent inequality.

## Key findings

- Counter-example to monotonicity and entropy comparison
- Complex analogue of Hao and Jog's dependent inequality
- Simplified proof of the complex analogue

## Abstract

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.