Jarzynski Equality for Conditional Stochastic Work
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.
- Authors:
-
[1];
[2]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States); Universidade Estadual de Campinas, Sao Paulo (Brazil)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1874914
- Report Number(s):
- LA-UR-20-28110
Journal ID: ISSN 0022-4715; TRN: US2307151
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Statistical Physics
- Additional Journal Information:
- Journal Volume: 183; Journal Issue: 1; Journal ID: ISSN 0022-4715
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics; Jarzynski equality, conditional stochastic work
Citation Formats
Sone, Akira, and Deffner, Sebastian. Jarzynski Equality for Conditional Stochastic Work. United States: N. p., 2021.
Web. doi:10.1007/s10955-021-02720-6.
Sone, Akira, & Deffner, Sebastian. Jarzynski Equality for Conditional Stochastic Work. United States. https://doi.org/10.1007/s10955-021-02720-6
Sone, Akira, and Deffner, Sebastian. Mon .
"Jarzynski Equality for Conditional Stochastic Work". United States. https://doi.org/10.1007/s10955-021-02720-6. https://www.osti.gov/servlets/purl/1874914.
@article{osti_1874914,
title = {Jarzynski Equality for Conditional Stochastic Work},
author = {Sone, Akira and Deffner, Sebastian},
abstractNote = {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.},
doi = {10.1007/s10955-021-02720-6},
journal = {Journal of Statistical Physics},
number = 1,
volume = 183,
place = {United States},
year = {Mon Apr 05 00:00:00 EDT 2021},
month = {Mon Apr 05 00:00:00 EDT 2021}
}
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