Jarzynski equality for conditional stochastic work

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https://link.springer.com/article/10.1007/s10955-021-02720-6

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http://hdl.handle.net/11603/20095
 https://doi.org/10.1007/s10955-021-02720-6

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UMBC Physics Department
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https://orcid.org/0000-0003-0504-6932

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journal articles
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Sone, Akira; Deffner, Sebastian; Jarzynski equality for conditional stochastic work; Journal of Statistical Physics, volume 183, number: 11, 5 April, 2021; https://doi.org/10.1007/s10955-021-02720-6

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This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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Abstract

It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose the conditional stochastic work for classical, Hamiltonian dynamics, which is inspired by the one-time measurement approach. This novel notion is built upon the change of expectation value of the energy conditioned on the initial energy surface. As main results we obtain a generalized Jarzynski equality and a sharper maximum work theorem, which account for how non-adiabatic the process is. Our findings are illustrated with the parametric harmonic oscillator.