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

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.

arXiv comment12 pages, 3 figures, comments welcome. v2 fixed typos and added some more remarks in discussion. Submission to SciPost

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