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Fundamental work cost of quantum processes

Faist, Philippe and Renner, Renato (2018) Fundamental work cost of quantum processes. Physical Review X, 8 (2). Art. No. 021011. ISSN 2160-3308. doi:10.1103/PhysRevX.8.021011.

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Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations.

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Additional Information:© 2018 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 5 September 2017; revised manuscript received 7 January 2018; published 10 April 2018. We are grateful to Mario Berta, Fernando Brandão, Frédéric Dupuis, Lea Krämer Gabriel, David Jennings, and Jonathan Oppenheim for discussions. We acknowledge contributions from the Swiss National Science Foundation (SNSF) via the NCCR QSIT as well as Project No. 200020_165843. P. F. acknowledges support from the SNSF through the Early PostDoc. Mobility Fellowship No. P2EZP2_165239 hosted by the Institute for Quantum Information and Matter (IQIM) at Caltech, as well as from the National Science Foundation.
Group:Institute for Quantum Information and Matter
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Swiss National Science Foundation (SNSF)200020_165843
Swiss National Science Foundation (SNSF)P2EZP2_165239
Issue or Number:2
Record Number:CaltechAUTHORS:20171102-133438149
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82902
Deposited By: Bonnie Leung
Deposited On:02 Nov 2017 21:32
Last Modified:15 Nov 2021 19:53

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