The geometry of passivity for quantum states and a novel elementary derivation of the Gibbs state
File(s)
Published version
Author(s)
Koukoulekidis, Nikolaos
Alexander, Rhea
Hebdige, Thomas
Jennings, David
Type
Journal Article
Abstract
Passivity is a fundamental concept that constitutes a necessary condition for any quantum system to attain thermodynamic equilibrium, and for a notion of temperature to emerge. While extensive work has been done that exploits this, the transition from passivity at a single-shot level to the completely passive Gibbs state is technically clear but lacks a good over-arching intuition. Here, we reformulate passivity for quantum systems in purely geometric terms. This description makes the emergence of the Gibbs state from passive states entirely transparent. Beyond clarifying existing results, it also provides novel analysis for non-equilibrium quantum systems. We show that, to every passive state, one can associate a simple convex shape in a 2-dimensional plane, and that the area of this shape measures the degree to which the system deviates from the manifold of equilibrium states. This provides a novel geometric measure of athermality with relations to both ergotropy and β--athermality.
Date Issued
2021-03-15
Date Acceptance
2021-02-26
Citation
Quantum: the open journal for quantum science, 2021, 5 (1), pp.1-24
ISSN
2521-327X
Publisher
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
Start Page
1
End Page
24
Journal / Book Title
Quantum: the open journal for quantum science
Volume
5
Issue
1
Copyright Statement
© Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. Some rights reserved. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
License URL
Identifier
https://quantum-journal.org/papers/q-2021-03-15-411/
Subjects
Science & Technology
Physical Sciences
Quantum Science & Technology
Physics, Multidisciplinary
Physics
Publication Status
Published
Article Number
411
Date Publish Online
2021-03-15