Quantum work beyond classical (commuting) limits

TL;DR

This paper explores how quantum Hamiltonian incompatibility can serve as a thermodynamic resource, enabling work extraction beyond classical limits in average work tasks.

Contribution

It introduces a framework for quantifying the advantage of incompatible Hamiltonians in work extraction tasks, surpassing classical bounds.

Findings

Incompatible Hamiltonian settings exceed classical work limits.

Classical devices are limited by free-energy constraints.

Quantum incompatibility provides a thermodynamic advantage.

Abstract

Free energy fixes the maximum work of a thermodynamic process once the state and Hamiltonian are specified. A work-extraction task asks a different question: how much average work can a single device realize across several preparations and Hamiltonian settings? A classical work device is one whose Hamiltonian settings are mutually commuting. We place every branch at its best free-energy-limited work envelope and derive the corresponding classical limit on the task average. For pure preparations, the source is specified only by pairwise maximal-energy constraints: for each pair, the intrinsic maximal average energy under one common normalized Hamiltonian is bounded as part of the task data, while the work device is otherwise microscopically unrestricted. The benchmark is optimized over arbitrary-dimensional classical implementations. Incompatible Hamiltonian settings exceed this limit, even though every branch remains bounded by its own free-energy maximum. The advantage therefore does not arise in any single process, but in the average work of the task: incompatible Hamiltonians realize a value that no classical work device can attain. Hamiltonian incompatibility is thus a thermodynamic resource for work extraction.