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

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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.

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[1] Michael J. Kewming, Mark T. Mitchison, and Gabriel T. Landi, "Diverging current fluctuations in critical Kerr resonators", Physical Review A 106 3, 033707 (2022).

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