# Bounds on chaos from the eigenstate thermalization hypothesis

## TL;DR

This paper demonstrates that the bound on chaos growth in quantum many-body systems naturally arises from the eigenstate thermalization hypothesis, linking two fundamental concepts of thermalization.

## Contribution

It establishes a direct connection between the chaos bound and the eigenstate thermalization hypothesis, unifying key ideas in quantum thermalization theory.

## Key findings

- The chaos bound follows from the structure of operator matrix elements.
- Eigenstate thermalization hypothesis underpins the chaos growth limit.
- The work unifies two paradigms of thermal behavior in quantum systems.

## Abstract

We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the eigenstate thermalization hypothesis. This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.