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The geometry of passivity for quantum states and a novel elementary derivation of the Gibbs state

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Title: The geometry of passivity for quantum states and a novel elementary derivation of the Gibbs state
Authors: Koukoulekidis, N
Alexander, R
Hebdige, T
Jennings, D
Item 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.
Issue Date: 15-Mar-2021
Date of Acceptance: 26-Feb-2021
URI: http://hdl.handle.net/10044/1/88377
DOI: 10.22331/q-2021-03-15-411
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.
Keywords: Science & Technology
Physical Sciences
Quantum Science & Technology
Physics, Multidisciplinary
Publication Status: Published
Article Number: 411
Online Publication Date: 2021-03-15
Appears in Collections:Physics
Faculty of Natural Sciences

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