Work fluctuations due to partial thermalizations in two-level systems

Maria Quadeer, Kamil Korzekwa, and Marco Tomamichel
Phys. Rev. E 103, 042141 – Published 28 April 2021

Abstract

We study work extraction processes mediated by finite-time interactions with an ambient bath—partial thermalizations—as continuous-time Markov processes for two-level systems. Such a stochastic process results in fluctuations in the amount of work that can be extracted and is characterized by the rate at which the system parameters are driven in addition to the rate of thermalization with the bath. We analyze the distribution of work for the case in which the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and a lower bound for the variance of work showing that such processes cannot be fluctuation-free in general. We also observe that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynski's fluctuation-dissipation relation for systems initially in equilibrium. Finally, we analyze work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations, and we obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.

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  • Received 28 January 2021
  • Revised 14 March 2021
  • Accepted 29 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042141

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Maria Quadeer1, Kamil Korzekwa2, and Marco Tomamichel3

  • 1Centre for Quantum Software and Information, School of Computer Science, University of Technology Sydney, Ultimo NSW 2007, Australia
  • 2Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
  • 3Department of Electrical and Computer Engineering & Centre for Quantum Technologies, National University of Singapore, Singapore 119077

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Issue

Vol. 103, Iss. 4 — April 2021

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