Fluctuation theorems for genuine quantum mechanical regimes

TL;DR

This paper extends quantum fluctuation theorems by incorporating the quantum nature of the acting system, revealing the influence of entanglement, coherence, and inertia on work fluctuations in quantum thermodynamics.

Contribution

It introduces a framework for fluctuation theorems that includes the quantum acting system and employs a work observable, advancing understanding of quantum work fluctuations.

Findings

Quantum coherence and entanglement affect work fluctuations.

Inertia influences the approach to mechanical equilibrium.

Derived fluctuation theorems for quantum and classical regimes.

Abstract

Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists of treating work as a stochastic variable and the acting system as an eminently classical device with a deterministic dynamics. Inspired by technological advances in the field of quantum machines, here we look for corrections to work fluctuations theorems when the acting system is allowed to enter the quantum domain. This entails including the acting system in the dynamics and letting it share a nonclassical state with the system acted upon. Moreover, favoring a mechanical perspective to this program, we employ a concept of work observable. For simplicity, we choose as theoretical platform the autonomous dynamics of a two-particle system with an elastic coupling. For some specific processes, we derive several fluctuation theorems within both the quantum and classical statistical arenas. In the quantum results, we find that, along with entanglement and quantum coherence, aspects of inertia also play a significant role since they regulate the route to mechanical equilibrium.