A measure of majorization emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression tha...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/7/073001 |
| _version_ | 1797751186709807104 |
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| author | D Egloff O C O Dahlsten R Renner V Vedral |
| author_facet | D Egloff O C O Dahlsten R Renner V Vedral |
| author_sort | D Egloff |
| collection | DOAJ |
| description | The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorization determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorization governs which evolutions can be realized via thermal interactions, whereas the non-decrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory. |
| first_indexed | 2024-03-12T16:43:51Z |
| format | Article |
| id | doaj.art-bd453de98329476792a8a32b77cf5eb9 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:43:51Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-bd453de98329476792a8a32b77cf5eb92023-08-08T14:19:55ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117707300110.1088/1367-2630/17/7/073001A measure of majorization emerging from single-shot statistical mechanicsD Egloff0O C O Dahlsten1R Renner2V Vedral3Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland; Institute for Theoretical Physics, Universität Ulm, D-89069 Ulm, GermanyAtomic and Laser Physics, Clarendon Laboratory , University of Oxford, Parks Road, Oxford OX13PU, UK; Center for Quantum Technologies, National University of Singapore , Republic of SingaporeInstitute for Theoretical Physics, ETH Zürich, 8093 Zurich, SwitzerlandAtomic and Laser Physics, Clarendon Laboratory , University of Oxford, Parks Road, Oxford OX13PU, UK; Center for Quantum Technologies, National University of Singapore , Republic of SingaporeThe use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorization determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorization governs which evolutions can be realized via thermal interactions, whereas the non-decrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.https://doi.org/10.1088/1367-2630/17/7/073001single-shot thermodynamicsentanglementmajorizationthermodynamics |
| spellingShingle | D Egloff O C O Dahlsten R Renner V Vedral A measure of majorization emerging from single-shot statistical mechanics New Journal of Physics single-shot thermodynamics entanglement majorization thermodynamics |
| title | A measure of majorization emerging from single-shot statistical mechanics |
| title_full | A measure of majorization emerging from single-shot statistical mechanics |
| title_fullStr | A measure of majorization emerging from single-shot statistical mechanics |
| title_full_unstemmed | A measure of majorization emerging from single-shot statistical mechanics |
| title_short | A measure of majorization emerging from single-shot statistical mechanics |
| title_sort | measure of majorization emerging from single shot statistical mechanics |
| topic | single-shot thermodynamics entanglement majorization thermodynamics |
| url | https://doi.org/10.1088/1367-2630/17/7/073001 |
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