# Geometric Fluctuation Theorem

## TL;DR

This paper derives an extended fluctuation theorem for geometric pumping in a spin-boson system under periodic temperature control, using quantum master equations and simulations to analyze current fluctuations.

## Contribution

It introduces a novel extended fluctuation theorem applicable to geometric pumping in quantum systems, highlighting differences from classical reciprocal relations.

## Key findings

- Derived an extended fluctuation theorem for quantum geometric pumping.
- Simulated current distributions and fluctuations in a spin-boson system.
- Found that the fluctuation theorem explains simulation results and relates to fluctuation dissipation.

## Abstract

We derive an extended fluctuation theorem for a geometric pumping in a spin-boson system under a periodic control of environmental temperatures by using a Markovian quantum master equation. We perform the Monte-Carlo simulation and obtain the current distribution, the average current and the fluctuation. Using the extended fluctuation theorem we try to explain the results of our simulation. The fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.