Quantum Coherence and Ergotropy

TL;DR

This paper investigates the role of quantum coherence in work extraction, specifically analyzing its contribution to ergotropy and providing bounds and examples relevant to quantum heat engines.

Contribution

It isolates the quantum coherent component of work yield in thermodynamic protocols and establishes bounds for coherent and incoherent work extraction.

Findings

Identifies a coherent contribution to ergotropy in quantum thermodynamic cycles.

Provides bounds for coherent and incoherent work extraction components.

Illustrates results with finite-dimensional and bosonic Gaussian systems.

Abstract

Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this non-equilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.