# Quantum Fluctuation Relations

## TL;DR

This paper discusses classical and quantum fluctuation relations, proving key theorems like Jarzynski and Crooks, and explores their similarities and differences in quantum systems.

## Contribution

It provides a detailed analysis of quantum fluctuation relations, extending classical results and highlighting their quantum-specific features.

## Key findings

- Proof of Jarzynski equality and Crooks fluctuation theorem
- Analysis of quantum versions of classical fluctuation relations
- Comparison of classical and quantum fluctuation relations

## Abstract

We present here a set of lecture notes on exact fluctuation relations. We prove the Jarzynski equality and the Crooks fluctuation theorem, two paradigmatic examples of classical fluctuation relations. Finally we consider their quantum versions, and analyze analogies and differences with the classical case.