Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature

Michael J. Kewming; Sally Shrapnel

doi:10.22331/q-2022-04-13-685

Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature

Michael J. Kewming¹ and Sally Shrapnel²

¹School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
²Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, QLD 4072 Australia

Published:	2022-04-13, volume 6, page 685
Eprint:	arXiv:2109.01998v3
Doi:	https://doi.org/10.22331/q-2022-04-13-685
Citation:	Quantum 6, 685 (2022).

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Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:

12 pages, 5 figures

Abstract

Fluctuation theorems allow one to make generalised statements about the behaviour of thermodynamic quantities in systems that are driven far from thermal equilibrium. In this article we use Crooks' fluctuation theorem to understand the entropy production of a continuously measured, zero temperature quantum system; namely an optical cavity measured via homodyne detection. At zero temperature, if one uses the classical definition of inverse temperature $\beta$, then the entropy production becomes divergent. Our analysis shows that the entropy production can be well defined at zero temperature by considering the entropy produced in the measurement record leading to an effective inverse temperature $\beta_{\rm eff}$ which does not diverge. We link this result to the Cramér-Rao inequality and show that the product of the Fisher information of the work distribution with the entropy production is bounded below by half of the square of the effective inverse temperature $\beta_{\rm eff}$. This inequality indicates that there is a minimal amount of entropy production that is paid to acquire information about the work done to a quantum system driven far from equilibrium.

► BibTeX data

@article{Kewming2022entropyproduction,
  doi = {10.22331/q-2022-04-13-685},
  url = {https://doi.org/10.22331/q-2022-04-13-685},
  title = {Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature},
  author = {Kewming, Michael J. and Shrapnel, Sally},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {685},
  month = apr,
  year = {2022}
}

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[2] Giorgio Zicari, Barış Çakmak, Özgür E Müstecaplıoğlu, and Mauro Paternostro, "On the role of initial coherence in the spin phase-space entropy production rate", New Journal of Physics 25 1, 013030 (2023).

[3] Laetitia P. Bettmann, Michael J. Kewming, and John Goold, "Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework", Physical Review E 107 4, 044102 (2023).

[4] Thales A. B. Pinto Silva and David Gelbwaser-Klimovsky, "Quantum work: Reconciling quantum mechanics and thermodynamics", Physical Review Research 6 2, L022036 (2024).

[5] Archak Purkayastha and Klaus Mølmer, "Nonclassical radiation from a nonlinear oscillator driven solely by classical 1/f noise", Physical Review A 108 5, 053704 (2023).

[6] L. S. Marinho, O. P. de Sá Neto, Marcos Sampaio, Helder A. S. Costa, and I. G. da Paz, "Open quantum behaviour manifested in the double-slit experiment", Europhysics Letters 143 4, 40001 (2023).

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[8] Knud Thomsen, "A heuristic sketch how it could fit all together with time", arXiv:2405.10335, (2024).

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