# Quantum Martingale Theory and Entropy Production

## TL;DR

This paper develops a quantum martingale framework to analyze entropy production fluctuations in open quantum systems, deriving universal fluctuation relations and validating them through numerical simulations.

## Contribution

It introduces a novel martingale approach to quantum entropy production, including a decomposition into quantum and classical parts, with universal fluctuation theorems for stopping times.

## Key findings

- Decomposition of entropy production into exponential martingale and quantum term
- Universal fluctuation relations for stopping-time and infimum statistics
- Numerical validation with a qubit system

## Abstract

We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into an exponential martingale and a purely quantum term, both obeying integral fluctuation theorems. An important consequence of this approach is the derivation of a set of genuine universal results for stopping-time and infimum statistics of stochastic entropy production. Finally we complement the general formalism with numerical simulations of a qubit system.