Finite-time bounds on the probabilistic violation of the second law of thermodynamics
Jarzynski's equality sets a strong bound on the probability of violating the second law of thermodynamics by extracting work beyond the free energy difference. We derive finite-time refinements to this bound for driven systems in contact with a thermal Markovian environment, which can be expres...
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| Format: | Article |
| Language: | English |
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SciPost
2023-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.4.072 |
| _version_ | 1827965622055600128 |
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| author | Harry J. D. Miller, Martí Perarnau-Llobet |
| author_facet | Harry J. D. Miller, Martí Perarnau-Llobet |
| author_sort | Harry J. D. Miller, Martí Perarnau-Llobet |
| collection | DOAJ |
| description | Jarzynski's equality sets a strong bound on the probability of violating the second law of thermodynamics by extracting work beyond the free energy difference. We derive finite-time refinements to this bound for driven systems in contact with a thermal Markovian environment, which can be expressed in terms of the geometric notion of thermodynamic length. We show that finite-time protocols converge to Jarzynski's bound at a rate slower than $1/\sqrt{\tau}$, where $\tau$ is the total time of the work-extraction protocol. Our result highlights a new application of minimal dissipation processes and demonstrates a connection between thermodynamic geometry and the higher order statistical properties of work. |
| first_indexed | 2024-04-09T17:37:24Z |
| format | Article |
| id | doaj.art-7dab84e6b507481cbf22ac745f26d8e5 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T17:37:24Z |
| publishDate | 2023-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-7dab84e6b507481cbf22ac745f26d8e52023-04-17T14:26:30ZengSciPostSciPost Physics2542-46532023-04-0114407210.21468/SciPostPhys.14.4.072Finite-time bounds on the probabilistic violation of the second law of thermodynamicsHarry J. D. Miller, Martí Perarnau-LlobetJarzynski's equality sets a strong bound on the probability of violating the second law of thermodynamics by extracting work beyond the free energy difference. We derive finite-time refinements to this bound for driven systems in contact with a thermal Markovian environment, which can be expressed in terms of the geometric notion of thermodynamic length. We show that finite-time protocols converge to Jarzynski's bound at a rate slower than $1/\sqrt{\tau}$, where $\tau$ is the total time of the work-extraction protocol. Our result highlights a new application of minimal dissipation processes and demonstrates a connection between thermodynamic geometry and the higher order statistical properties of work.https://scipost.org/SciPostPhys.14.4.072 |
| spellingShingle | Harry J. D. Miller, Martí Perarnau-Llobet Finite-time bounds on the probabilistic violation of the second law of thermodynamics SciPost Physics |
| title | Finite-time bounds on the probabilistic violation of the second law of thermodynamics |
| title_full | Finite-time bounds on the probabilistic violation of the second law of thermodynamics |
| title_fullStr | Finite-time bounds on the probabilistic violation of the second law of thermodynamics |
| title_full_unstemmed | Finite-time bounds on the probabilistic violation of the second law of thermodynamics |
| title_short | Finite-time bounds on the probabilistic violation of the second law of thermodynamics |
| title_sort | finite time bounds on the probabilistic violation of the second law of thermodynamics |
| url | https://scipost.org/SciPostPhys.14.4.072 |
| work_keys_str_mv | AT harryjdmillermartiperarnaullobet finitetimeboundsontheprobabilisticviolationofthesecondlawofthermodynamics |