Coherent fluctuation relations: from the abstract to the concrete

Zoë Holmes1, Sebastian Weidt2, David Jennings1,3,4, Janet Anders5, and Florian Mintert1

1Controlled Quantum Dynamics Theory Group, Imperial College London, London, SW7 2BW, United Kingdom.
2Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom.
3Department of Physics, University of Oxford, Oxford, OX1 3PU, United Kingdom.
4School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom.
5CEMPS, Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, United Kingdom.

Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for well-known coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.

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Cited by

[1] Matteo Lostaglio, "Thermodynamic laws for populations and quantum coherence: A self-contained introduction to the resource theory approach to thermodynamics", arXiv:1807.11549 (2018).

[2] Hyukjoon Kwon and M. S. Kim, "Fluctuation Theorem for an Arbitrary Quantum Process", arXiv:1810.03150 (2018).

[3] Juliette Monsel, Cyril Elouard, and Alexia Auffèves, "An autonomous quantum machine to measure the thermodynamic arrow of time", npj Quantum Information 4, 59 (2018).

[4] Erick Hinds Mingo and David Jennings, "Superpositions of mechanical processes, decomposable coherence and fluctuation relations", arXiv:1812.08159 (2018).

[5] Zoe Holmes, "The Coherent Crooks Equality", Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions 195, 301 (2018).

[6] Nicole Yunger Halpern and David T. Limmer, "Fundamental limitations on photoisomerization from thermodynamic resource theories", arXiv:1811.06551 (2018).

[7] Álvaro M. Alhambra, Matteo Lostaglio, and Christopher Perry, "Heat-Bath Algorithmic Cooling with Thermal Operations", arXiv:1807.07974 (2018).

[8] Martí Perarnau-Llobet, "Quantum signatures in fluctuation theorems", Quantum Views 3, 13 (2019).

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