# Energy extraction of a chaotic system in a cyclic process: a Szil\'ard Engine perspective

## TL;DR

This paper proposes a cyclic process in a chaotic system inspired by Szilard Engines, demonstrating energy extraction through numerical simulations and theoretical analysis, and explores the role of symmetry breaking in such energy decreases.

## Contribution

It introduces a new chaotic system with a cyclic process that reduces average energy, extending Szilard Engine concepts to chaotic dynamics and analyzing symmetry breaking effects.

## Key findings

- Average energy decreases after a cycle in the proposed system
- Numerical simulations confirm the energy decrement predicted by theory
- Symmetry breaking may enable energy extraction in chaotic systems

## Abstract

Inspired by the available examples of Microcanonical Szil\'ard Engines and by the original Szil\'ard Engine, we devise a system with two degrees of freedom whose ensemble average energy, starting with a microcanical ensemble, decreases after a cyclic variation of its external parameters. We use the Ergodic Adiabatic Theorem to motivate our cycle and numerical simulations to check the decrement in the average energy. We then compare our system to the aforementioned Szil\'ard Engines, Microcanonical or not, and speculate about symmetry breaking being the cause of energy extraction in cyclic processes, even when non-integrability and chaos are present.