# Decomposable coherence and quantum fluctuation relations

## TL;DR

This paper introduces the concept of coherent work processes in quantum mechanics, extending classical work processes, and explores their role in quantum fluctuation relations, coherence, and entanglement.

## Contribution

It defines decomposable and non-decomposable quantum coherence and connects these to fluctuation relations and classical thermodynamics.

## Key findings

- Coherent work processes mirror classical counterparts in quantum systems.
- Introduction of a pure state effective potential for analyzing quantum coherence.
- Hierarchy of quantum corrections to Crooks relation based on temperature.

## Abstract

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process', and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable' and `non-decomposable' quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.