Relative entropy formulation of thermalization process in a Schwarzschild spacetime
We revisit the problem of the thermalization process in an entropic formulation for the Unruh-DeWitt (UDW) detector outside a Schwarzschild black hole. We derive the late-time dynamics of the detector in the context of open quantum system, and capture the path distinguishability and thermodynamic ir...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269324007937 |
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| author | Si-Wei Han Zhichun Ouyang Zhiyao Hu Jun Feng |
| author_facet | Si-Wei Han Zhichun Ouyang Zhiyao Hu Jun Feng |
| author_sort | Si-Wei Han |
| collection | DOAJ |
| description | We revisit the problem of the thermalization process in an entropic formulation for the Unruh-DeWitt (UDW) detector outside a Schwarzschild black hole. We derive the late-time dynamics of the detector in the context of open quantum system, and capture the path distinguishability and thermodynamic irreversibility of detector thermalization process by using quantum relative entropy (QRE). We find that beyond the Planckian transition rate, the refined thermalization process in detector Hilbert space can be distinguished by the time behavior of the related QRE. We show that the exotic position-dependent behaviors of the QRE emerge corresponding to different choices of black hole vacua (i.e., the Boulware, Hartle-Hawking, and Unruh vacua). Finally, from a perspective of quantum thermodynamics, we recast the free energy change of the UDW detector undergoing Hawking radiation into an entropic combination form, where the classical Kullback-Leibler divergence and quantum coherence are presented in specific QRE-like forms. With growing Hawking temperature, we find that the consumption rate of quantum coherence is larger than that of its classical counterpart. |
| format | Article |
| id | doaj-art-32742170852546b7b57dd2bd6ce29f61 |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-32742170852546b7b57dd2bd6ce29f612025-02-10T04:33:50ZengElsevierPhysics Letters B0370-26932025-02-01861139235Relative entropy formulation of thermalization process in a Schwarzschild spacetimeSi-Wei Han0Zhichun Ouyang1Zhiyao Hu2Jun Feng3School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, ChinaSchool of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China; Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region of ChinaSchool of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, ChinaSchool of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China; Institute of Theoretical Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China; Corresponding author at: School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China.We revisit the problem of the thermalization process in an entropic formulation for the Unruh-DeWitt (UDW) detector outside a Schwarzschild black hole. We derive the late-time dynamics of the detector in the context of open quantum system, and capture the path distinguishability and thermodynamic irreversibility of detector thermalization process by using quantum relative entropy (QRE). We find that beyond the Planckian transition rate, the refined thermalization process in detector Hilbert space can be distinguished by the time behavior of the related QRE. We show that the exotic position-dependent behaviors of the QRE emerge corresponding to different choices of black hole vacua (i.e., the Boulware, Hartle-Hawking, and Unruh vacua). Finally, from a perspective of quantum thermodynamics, we recast the free energy change of the UDW detector undergoing Hawking radiation into an entropic combination form, where the classical Kullback-Leibler divergence and quantum coherence are presented in specific QRE-like forms. With growing Hawking temperature, we find that the consumption rate of quantum coherence is larger than that of its classical counterpart.http://www.sciencedirect.com/science/article/pii/S0370269324007937 |
| spellingShingle | Si-Wei Han Zhichun Ouyang Zhiyao Hu Jun Feng Relative entropy formulation of thermalization process in a Schwarzschild spacetime Physics Letters B |
| title | Relative entropy formulation of thermalization process in a Schwarzschild spacetime |
| title_full | Relative entropy formulation of thermalization process in a Schwarzschild spacetime |
| title_fullStr | Relative entropy formulation of thermalization process in a Schwarzschild spacetime |
| title_full_unstemmed | Relative entropy formulation of thermalization process in a Schwarzschild spacetime |
| title_short | Relative entropy formulation of thermalization process in a Schwarzschild spacetime |
| title_sort | relative entropy formulation of thermalization process in a schwarzschild spacetime |
| url | http://www.sciencedirect.com/science/article/pii/S0370269324007937 |
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