# Work fluctuations in slow processes: quantum signatures and optimal control

## TL;DR

This paper reveals that quantum coherence causes violations of classical work fluctuation-dissipation relations in slow processes, leading to non-Gaussian work distributions and a fundamental trade-off between dissipation and fluctuations, addressed through a quantum geometric framework.

## Contribution

It introduces a quantum generalisation of the work fluctuation-dissipation relation and develops a geometric method to optimize the balance between dissipation and fluctuations in slow quantum processes.

## Key findings

- Quantum coherence leads to violations of classical FDR.
- Work distribution becomes non-Gaussian due to quantum effects.
- A quantum geometric framework optimizes the dissipation-fluctuation trade-off.

## Abstract

An important result in classical stochastic thermodynamics is the work fluctuation--dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations. Here we show that slowly driven quantum systems violate this FDR whenever quantum coherence is generated along the protocol, and derive a quantum generalisation of the work FDR. The additional quantum terms in the FDR are found to lead to a non-Gaussian work distribution. Fundamentally, our result shows that quantum fluctuations prohibit finding slow protocols that minimise both dissipation and fluctuations simultaneously, in contrast to classical slow processes. Instead, we develop a quantum geometric framework to find processes with an optimal trade-off between the two quantities.