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

TL;DR

This paper refines the bounds on the probability of violating the second law of thermodynamics in finite-time processes, linking thermodynamic length with work fluctuations in driven systems.

Contribution

It derives finite-time bounds on thermodynamic violations using thermodynamic length, extending Jarzynski's equality to non-infinite protocols.

Findings

Finite-time protocols converge to Jarzynski's bound at a rate slower than 1/√τ

Introduces a geometric approach to thermodynamic bounds

Connects thermodynamic geometry with work fluctuation statistics

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.