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

by Harry J. D. Miller, Martí Perarnau-Llobet

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Harry Miller
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-01-10
Date submitted: 2022-11-30 13:09
Submitted by: Miller, Harry
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Published as SciPost Phys. 14, 072 (2023)

Author comments upon resubmission

We thank the referees for their careful reading of the manuscript and constructive comments. We have now added some additional clarifications in the paper regarding some of the referee remarks as listed below.

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).

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