ImpossibleWork-PRAJan2018.pdf (419.31 kB)
Quantum work in the Bohmian framework
journal contribution
posted on 2018-05-30, 08:08 authored by Rui Sampaio, Samu Suomela, Tapio Ala-NissilaTapio Ala-Nissila, J. Anders, T.G. PhilbinAt nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.
Funding
This work has been in part supported by the Academy of Finland through its CoE grants 284621 and 287750. R.S. acknowledges support from the Magnus Ehrnrooth Foundation. J.A. acknowledges support from EPSRC (grant EP/M009165/1) and the Royal Society. This research was supported by the COST network MP1209 “Thermodynamics in the quantum regime”.
History
School
- Science
Department
- Mathematical Sciences
Published in
Physical Review AVolume
97Issue
1Citation
SAMPAIO, R. ... et al, 2018. Quantum work in the Bohmian framework. Physical Review A, 97 (1), 012131.Publisher
© American Physical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2018Notes
This paper was published in the journal Physical Review A and the definitive published version is available at https://doi.org/10.1103/PhysRevA.97.012131.ISSN
2469-9926eISSN
2469-9934Publisher version
Language
- en