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2022-07-23Zeitschriftenartikel DOI: 10.3390/e24081016
Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
dc.contributor.authorReiche, Daniel
dc.contributor.authorHsiang, Jen-Tsung
dc.contributor.authorHu, Bei-Lok
dc.contributor.editorKosloff, Ronnie
dc.date.accessioned2022-08-08T10:42:04Z
dc.date.available2022-08-08T10:42:04Z
dc.date.issued2022-07-23none
dc.date.updated2022-08-03T10:46:34Z
dc.identifier.urihttp://edoc.hu-berlin.de/18452/25771
dc.description.abstractThermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.eng
dc.description.sponsorshipFederal Ministry for Economic Affairs and Climate Action (BMWK)
dc.description.sponsorshipMinistry of Science and Technology of Taiwan, R.O.C.
dc.description.sponsorshipDeutsche Forschungsgemeinschaft (DFG, German Research Foundation)
dc.description.sponsorshipOpen Access Publication Fund of Humboldt-Universität zu Berlin
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY 4.0) Attribution 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectThermodynamic Uncertainty Relationeng
dc.subjectnonequilibrium field theoryeng
dc.subjectquantum thermodynamic uncertaintieseng
dc.subjectRobertson–Schrödinger uncertainty principleeng
dc.subjectFluctuation-Dissipation Inequalityeng
dc.subject.ddc530 Physiknone
dc.titleQuantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalitiesnone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/25771-3
dc.identifier.doi10.3390/e24081016none
dc.identifier.doihttp://dx.doi.org/10.18452/25087
dc.type.versionpublishedVersionnone
local.edoc.container-titleEntropynone
local.edoc.pages35none
local.edoc.anmerkungThis article was supported by the German Research Foundation (DFG) and the Open Access Publication Fund of Humboldt-Universität zu Berlin.
local.edoc.type-nameZeitschriftenartikel
local.edoc.institutionMathematisch-Naturwissenschaftliche Fakultätnone
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-nameMDPInone
local.edoc.container-publisher-placeBaselnone
local.edoc.container-volume24none
local.edoc.container-issue8none
local.edoc.container-year2022none
dc.description.versionPeer Reviewednone
local.edoc.container-articlenumber1016none
dc.identifier.eissn1099-4300

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