Model Studies on the Quantum Jarzynski Relation

TL;DR

This paper extends the quantum Jarzynski relation to various open quantum systems, providing proofs for different coupling scenarios and validating the results through numerical simulations.

Contribution

It generalizes the proof of the quantum Jarzynski relation to bipartite systems with microcanonical and canonical coupling, including open systems at high temperatures.

Findings

Jarzynski relation holds for bipartite systems with microcanonical coupling.

Relation is valid for open systems at high initial temperatures.

Numerical simulations support the analytical results.

Abstract

We study the quantum Jarzynski relation for driven quantum models embedded in various environments. We do so by generalizing a proof presented by Mukamel [Phys. Rev. Lett 90, 170604 (2003)] for closed quantum systems. In this way, we are able to prove that the Jarzynski relation also holds for a bipartite system with microcanonical coupling. Furthermore, we show that, under the assumption that the interaction energy remains constant during the whole process, the relation is valid even for canonical coupling. The same follows for open quantum systems at high initial temperatures up to third order of the inverse temperature. Our analytical study is complemented by a numerical investigation of a special model system.