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Finite-time bounds on the probabilistic violation of the second law of thermodynamics
by Harry J. D. Miller, Martà Perarnau-Llobet
Submission summary
| Authors (as registered SciPost users): | Harry J. D. Miller |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2205.03065v2 (pdf) |
| Date accepted: | Jan. 10, 2023 |
| Date submitted: | Nov. 30, 2022, 1:09 p.m. |
| Submitted by: | Harry J. D. Miller |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author comments upon resubmission
List of changes
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We have specified that we assume no degeneracies in the system Hamiltonian, below Eq. (50).
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A remark about the different scalings for average dissipation and the cumulative distribution has been added to discussion, alongside an additional reference [46].
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Corrected a minor typo in Eq. (66).
Published as SciPost Phys. 14, 072 (2023)