Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study th...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Online Access: | https://www.mdpi.com/1099-4300/23/12/1602 |
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| author | Jin-Fu Chen Tian Qiu Hai-Tao Quan |
| author_facet | Jin-Fu Chen Tian Qiu Hai-Tao Quan |
| author_sort | Jin-Fu Chen |
| collection | DOAJ |
| description | Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements. |
| first_indexed | 2024-03-10T04:10:50Z |
| format | Article |
| id | doaj.art-1e27249d290148dcb6924a41bf5f62c5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T04:10:50Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-1e27249d290148dcb6924a41bf5f62c52023-11-23T08:10:29ZengMDPI AGEntropy1099-43002021-11-012312160210.3390/e23121602Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian MotionJin-Fu Chen0Tian Qiu1Hai-Tao Quan2School of Physics, Peking University, Beijing 100871, ChinaSchool of Physics, Peking University, Beijing 100871, ChinaSchool of Physics, Peking University, Beijing 100871, ChinaQuantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.https://www.mdpi.com/1099-4300/23/12/1602open quantum systemsphase-space formulationquantum Brownian motionheat statistics |
| spellingShingle | Jin-Fu Chen Tian Qiu Hai-Tao Quan Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion Entropy open quantum systems phase-space formulation quantum Brownian motion heat statistics |
| title | Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion |
| title_full | Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion |
| title_fullStr | Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion |
| title_full_unstemmed | Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion |
| title_short | Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion |
| title_sort | quantum classical correspondence principle for heat distribution in quantum brownian motion |
| topic | open quantum systems phase-space formulation quantum Brownian motion heat statistics |
| url | https://www.mdpi.com/1099-4300/23/12/1602 |
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