Extracting work from quantum systems

TL;DR

This paper demonstrates that in quantum thermodynamics, classical states allow for single-copy work extraction matching free energy, while non-classical states require collective actions, highlighting the nuanced role of quantum coherence.

Contribution

It introduces protocols for work extraction in quantum systems that match classical thermodynamics results for classical states and clarifies the necessity of collective actions for non-classical states.

Findings

Single-copy work extraction equals free energy for classical states.

Collective actions are necessary for extracting work from non-classical states.

The notion of free energy remains meaningful at the single-system level.

Abstract

We consider the task of extracting work from quantum systems in the resource theory perspective of thermodynamics, where free states are arbitrary thermal states, and allowed operations are energy conserving unitary transformations. Taking as our work storage system a 'weight' we prove the second law and then present simple protocols which extract average work equal to the free energy change of the system - the same amount as in classical thermodynamics. Crucially, for systems in 'classical' states (mixtures of energy eigenstates) our protocol works on a single copy of the system. This is in sharp contrast to previous results, which showed that in case of almost-deterministic work extraction, collective actions on multiple copies are necessary to extract the free energy. This establishes the fact that free energy is a meaningful notion even for individual systems in classical states. However, for non-classical states, where coherences between energy levels exist, we prove that collective actions are necessary, so long as no external sources of coherence are used.