Abstract
Modern quantum experiments provide examples of transport with noncommuting quantities, offering a tool to understand the interplay between thermal and quantum effects. Here we set forth a theory for non-Abelian transport in the linear response regime. Our key insight is to use generalized Gibbs ensembles with noncommuting charges as the basic building blocks and strict charge-preserving unitaries in a collisional setup. The linear response framework is then built using a collisional model between two reservoirs. We show that the transport coefficients obey Onsager reciprocity. Moreover, we find that quantum coherence, associated with the noncommutativity, acts so as to reduce the net entropy production, when compared to the case of commuting transport. This therefore provides a clear connection between quantum coherent transport and dissipation. As an example, we study heat and squeezing fluxes in bosonic systems, characterizing a set of thermosqueezing coefficients with potential applications in metrology and heat-to-work conversion in the quantum regime.Received 13 November 2020Revised 16 March 2021Accepted 6 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010304Published 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.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium & irreversible thermodynamicsQuantum coherence & coherence measuresQuantum thermodynamicsQuantum transportSqueezing of quantum noisePhysical SystemsQuantum heat engines & refrigeratorsTechniquesInformation theoryLinear response theoryQuantum InformationStatistical PhysicsAtomic, Molecular & Optical
Highlights
In the simplest scenario, putting in contact two thermal systems at different temperatures causes them to exchange heat [1]
To compute L, we have developed a method based on the so-called symmetric logarithmic derivative (SLD)
We formulated a general framework based on a collisional model, and derived Onsager reciprocity relations for non-Abelian transport in linear response
Summary
In the simplest scenario, putting in contact two thermal systems at different temperatures causes them to exchange heat [1]. Since exchanges of extra conserved quantities may contribute to both heat and work, non-Abelian transport theory may help to clarify the thermodynamics of squeezing-powered engines [40,41,42,43] and other nonthermal devices [44,45,46]. Our results show that the transport coefficients, as well as the entropy production, can be written in terms of the so-called y covariances [48,49,50,51,52], which provide a generalization of the notion of covariances to noncommuting observables This is further expressed in terms of the Wigner-Yanase-Dyson skew information [49], a quantifier of quantum coherence. The interesting avenues of research this opens are exemplified by metrology in a squeezing-based thermocouple, and heat-to-work conversion in an autonomous engine
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