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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
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Harry Miller |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2205.03065v2 (pdf) |
| Date accepted: | 2023-01-10 |
| Date submitted: | 2022-11-30 13:09 |
| Submitted by: | Miller, Harry |
| 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
1. We have specified that we assume no degeneracies in the system Hamiltonian, below Eq. (50).
2. A remark about the different scalings for average dissipation and the cumulative distribution has been added to discussion, alongside an additional reference [46].
3. Corrected a minor typo in Eq. (66).
Published as SciPost Phys. 14, 072 (2023)