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 |
| Summary: | 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. |
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| ISSN: | 2542-4653 |