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dc.contributor.authorPolkovnikov, Anatolien_US
dc.date.accessioned2019-08-26T18:33:57Z
dc.date.available2019-08-26T18:33:57Z
dc.date.issued2011-02-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000287015700014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationAnatoli Polkovnikov. 2011. "Microscopic diagonal entropy and its connection to basic thermodynamic relations." ANNALS OF PHYSICS, Volume 326, Issue 2, pp. 486 - 499 (14). https://doi.org/10.1016/j.aop.2010.08.004
dc.identifier.issn0003-4916
dc.identifier.urihttps://hdl.handle.net/2144/37351
dc.description.abstractWe define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as Sd = − 𝛴𝑛 𝘗𝑛𝑛 l𝑛 𝘗𝘯𝘯 with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy Sn = −Trρ ln ρ. However, in contrast to Sn, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that Sd behaves consistently with expectations from thermodynamics.en_US
dc.description.sponsorshipThe author acknowledges helpful discussions with R. Barankov on earlier stages of this work. The author also thanks C. Gogolin for sharing the proof of Eq. (24) and for many valuable comments. It is also a pleasure to acknowledge E. Altman, S. Girvin, V. Gritsev, V. Gurarie, D. Huse, Y. Kafri, W. Zwerger for helpful discussions related to this work. This work was supported by NSF (DMR-0907039), AFOSR YIP, AFOSR FA9550-10-1-0110, and Sloan Foundation. (DMR-0907039 - NSF; AFOSR YIP; FA9550-10-1-0110 - AFOSR; Sloan Foundation)en_US
dc.format.extentp. 486 - 499en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCEen_US
dc.relation.ispartofANNALS OF PHYSICS
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectPhysics, multidisciplinaryen_US
dc.subjectPhysicsen_US
dc.subjectStatistical mechanicsen_US
dc.subjectThermodynamicsen_US
dc.subjectQuantum dynamicsen_US
dc.subjectHamiltonian systemsen_US
dc.subjectSystemsen_US
dc.subjectStatistical mechanicsen_US
dc.subjectQuantum dynamicsen_US
dc.subjectMathematical sciencesen_US
dc.subjectPhysical sciencesen_US
dc.subjectNuclear & particles physicsen_US
dc.titleMicroscopic diagonal entropy and its connection to basic thermodynamic relationsen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1016/j.aop.2010.08.004
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Physicsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-5549-7400 (Polkovnikov, Anatoli)
dc.identifier.mycv54776


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