Optimal local work extraction from bipartite quantum systems in the presence of Hamiltonian couplings

TL;DR

This paper explores the maximum work extractable from bipartite quantum systems via local unitaries, providing formulas, bounds, and applications to quantum systems like cavities and spin chains.

Contribution

It introduces a closed-form expression for local ergotropy in two-level systems and offers bounds for general cases, advancing understanding of work extraction in quantum thermodynamics.

Findings

Closed formula for local ergotropy in two-level systems

Bounds for local ergotropy in general bipartite systems

Work extraction can surpass that from decoupling the system from its environment

Abstract

We investigate the problem of finding the local analogue of the ergotropy, that is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and give analytic lower bounds and semidefinite programming upper bounds for the general case. As non-trivial examples of application, we compute the local ergotropy for a atom in an electromagnetic cavity with Jaynes-Cummings coupling, and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with an unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation.