Finite-time bounds on the probabilistic violation of the second law of thermodynamics

• URL: http://arxiv.org/abs/2205.03065v2
• Date: Tue, 29 Nov 2022 14:11:18 GMT
• Title: Finite-time bounds on the probabilistic violation of the second law of thermodynamics
• Authors: Harry J. D. Miller, Mart\'i Perarnau-Llobet
• Abstract summary: We show that finite-time protocols converge to Jarzynski's bound at a rate slower than $1/sqrttau$, 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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