Reconciliation of quantum local master equations with thermodynamics
The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially...
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| Published in | New journal of physics Vol. 20; no. 11; pp. 113024 - 113039 |
|---|---|
| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Bristol
IOP Publishing
16.11.2018
Institute of Physics: Open Access Journals |
| Subjects | |
| Online Access | Get full text |
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| Abstract | The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics. |
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| AbstractList | The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics. |
| Author | De Chiara, Gabriele Roncaglia, Augusto J Antezza, Mauro Hewgill, Adam Reid, Brendan Ferraro, Alessandro Landi, Gabriel |
| Author_xml | – sequence: 1 givenname: Gabriele orcidid: 0000-0003-3265-9021 surname: De Chiara fullname: De Chiara, Gabriele email: g.dechiara@qub.ac.uk organization: University of California Kavli Institute of Theoretical Physics (KITP), Santa Barbara CA 93106-4030, United States of America – sequence: 2 givenname: Gabriel surname: Landi fullname: Landi, Gabriel organization: Instituto de Física da Universidade de São Paulo , 05314-970 São Paulo, Brazil – sequence: 3 givenname: Adam surname: Hewgill fullname: Hewgill, Adam organization: Queen's University Belfast Centre for Theoretical Atomic, Molecular and Optical Physics, Belfast BT7 1NN, United Kingdom – sequence: 4 givenname: Brendan surname: Reid fullname: Reid, Brendan organization: Queen's University Belfast Centre for Theoretical Atomic, Molecular and Optical Physics, Belfast BT7 1NN, United Kingdom – sequence: 5 givenname: Alessandro surname: Ferraro fullname: Ferraro, Alessandro organization: Queen's University Belfast Centre for Theoretical Atomic, Molecular and Optical Physics, Belfast BT7 1NN, United Kingdom – sequence: 6 givenname: Augusto J surname: Roncaglia fullname: Roncaglia, Augusto J organization: Ciudad Universitaria Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, 1428 Buenos Aires, Argentina – sequence: 7 givenname: Mauro orcidid: 0000-0003-4540-5864 surname: Antezza fullname: Antezza, Mauro organization: Institut Universitaire de France , 1 rue Descartes, F-75231 Paris Cedex 05, France |
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| SubjectTerms | Atomic and Molecular Clusters Atomic Physics Collisions Condensed Matter Harmonic oscillators Heat engines master equations Mathematical models open quantum systems Optics Physics Quantum Gases quantum harmonic oscillators Quantum Physics quantum thermodynamics Subsystems Thermodynamics |
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| Title | Reconciliation of quantum local master equations with thermodynamics |
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