Sharpening the second law of thermodynamics with the quantum Bayes theorem
We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law...
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| Format: | Article |
| Language: | English |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/90265 https://orcid.org/0000-0001-7670-7190 |
| _version_ | 1826200218787381248 |
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| author | Gharibyan, Hrant Tegmark, Max Erik |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Gharibyan, Hrant Tegmark, Max Erik |
| author_sort | Gharibyan, Hrant |
| collection | MIT |
| description | We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies. |
| first_indexed | 2024-09-23T11:33:02Z |
| format | Article |
| id | mit-1721.1/90265 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:33:02Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/902652022-09-27T20:15:03Z Sharpening the second law of thermodynamics with the quantum Bayes theorem Gharibyan, Hrant Tegmark, Max Erik Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Gharibyan, Hrant Tegmark, Max Erik We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies. National Science Foundation (U.S.) (Grant AST-1105835) Massachusetts Institute of Technology. Undergraduate Research Opportunities Program 2014-09-22T18:02:30Z 2014-09-22T18:02:30Z 2014-09 2014-05 2014-09-19T22:00:02Z Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/90265 Gharibyan, Hrant, and Max Tegmark. "Sharpening the second law of thermodynamics with the quantum Bayes theorem." Phys. Rev. E 90, 032125 (September 2014). © 2014 American Physical Society https://orcid.org/0000-0001-7670-7190 en http://dx.doi.org/10.1103/PhysRevE.90.032125 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Gharibyan, Hrant Tegmark, Max Erik Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title | Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title_full | Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title_fullStr | Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title_full_unstemmed | Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title_short | Sharpening the second law of thermodynamics with the quantum Bayes theorem |
| title_sort | sharpening the second law of thermodynamics with the quantum bayes theorem |
| url | http://hdl.handle.net/1721.1/90265 https://orcid.org/0000-0001-7670-7190 |
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