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Maximum one-shot dissipated work from Rényi divergences

Yunger Halpern, Nicole and Garner, Andrew J. P. and Dahlsten, Oscar C. O. and Vedral, Vlatko (2018) Maximum one-shot dissipated work from Rényi divergences. Physical Review E, 97 (5). Art. No. 052135. ISSN 2470-0045. http://resolver.caltech.edu/CaltechAUTHORS:20150622-113733758

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Abstract

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevE.97.052135DOIArticle
https://arxiv.org/abs/1505.06217arXivDiscussion Paper
ORCID:
AuthorORCID
Yunger Halpern, Nicole0000-0001-8670-6212
Alternate Title:What’s the worst that could happen? One-shot dissipated work from Rényi divergences
Additional Information:© 2018 American Physical Society. Received 19 July 2017; published 25 May 2018. This work was supported by a Virginia Gilloon Fellowship; an IQIM Fellowship; a Barbara Groce Fellowship; a KITP Graduate Fellowship; NSF Grants No. PHY-0803371, No. PHY-1125565, and No. PHY-1125915; the Foundational Questions Institute (FQXi) Large Grants for “Time and the Structure of Quantum Theory” and “the Physics of the Observer” (FQXi-RFP-1614) the EPSRC; the John Templeton Foundation Grant 54914; the Leverhulme Trust; the Oxford Martin School; the NRF (Singapore); and the MoE (Singapore). The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation (GBMF-2644). V.V. and O.D. acknowledge funding from the EU Collaborative Project TherMiQ (Grant Agreement No. 618074). N.Y.H. thanks Ning Bao for conversations about high-energy scenarios. We thank all our referees for feedback, which enhanced this article.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Virginia Gilloon FellowshipUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Barbara Groce Graduate Fellowship, CaltechUNSPECIFIED
Kavli Institute for Theoretical PhysicsUNSPECIFIED
NSFPHY-0803371
NSFPHY-1125565
NSFPHY-1125915
Foundational Questions Institute (FQXI)FQXi-RFP-1614
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
John Templeton FoundationUNSPECIFIED
Leverhulme TrustUNSPECIFIED
Oxford Martin SchoolUNSPECIFIED
National Research Foundation (Singapore)UNSPECIFIED
Ministry of Education (Singapore)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-2644
European Research Council (ERC)618074
Record Number:CaltechAUTHORS:20150622-113733758
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150622-113733758
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58402
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2015 19:57
Last Modified:04 Dec 2018 19:25

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