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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. doi:10.1103/PhysRevE.97.052135.

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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
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URLURL TypeDescription Paper
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:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Virginia Gilloon FellowshipUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Barbara Groce Graduate Fellowship, CaltechUNSPECIFIED
Kavli Institute for Theoretical PhysicsUNSPECIFIED
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
Issue or Number:5
Record Number:CaltechAUTHORS:20150622-113733758
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58402
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2015 19:57
Last Modified:10 Nov 2021 22:04

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